Introduction to Micro Economics

indiscriminate curve

The value of u ₁ (x) + u ₂ (y) can not be specifically calculated but plotting points giving the same utility can do. When consumption amount of item 1 is increased, total utility will rise unless consumption amount of item 2 changes. The point of bringing the same utility must be in the lower right direction. Specifically, it can be seen that even if it can not be calculated, it becomes a curve going down to the right. The plot of the points that give the same utility is called indiscriminate curve. Enter an indiscriminate curve that brings several same utilities. The indifference curve located on the upper right has higher utility value. The optimal consumption plan is a consumption plan on an indifference curve that contacts the boundary of the budget constraint area in the figure. Because there is indiscriminate on the curve, there are countless combinations of consumption of goods 1 and 2. Do actual consumers do this kind of calculation? Regarding the optimal allocation by two products, namely product 1 and product 2, it is possible to intuitively decide the respective consumption amounts with the above-mentioned concept intuitively without performing precise calculation.

consumption plan

Optimal consumption plan

If you continue to consume a good or service, the utility value will rise, but eventually the degree of rise will decrease and eventually will not rise. Even if the utility value reaches its peak, such expenses will increase in proportion to consumption. There are various goods and services in the world. It is natural that you want to consume this too, and it is usual not to consume large quantities only for specific goods services due to budget constraints. Consumption planning is set up to optimally allocate the budget and obtain utility from various goods services. Once formulated, it solves the maximization problem of total utility received from various goods and service consumption under budget constraints, and determines the amount of various goods and service consumption.

As a more generalized expression, the consumer expresses the amount and quantity of various kinds of things and services (such as A goods, B goods, C goods) in the world by the following expression it can.

Additional benefits of A goods / Additional costs of A goods = Additional utility of goods B / Additional costs of goods B = Additional utilities of goods C / Additional costs of C goods

Consider the condition when total utility is maximized. x , y , y , Y , Y z Let's assume that it is in the optimum state when it is consuming. At this time, p _x x + p _y y + p _z z = I . u (x) + u (y) + u (z) is maximized. In order to increase x by 1, y or z from the budget constraint to p _x / p _y (or p _x / p _z ). p _y + u (z) / p _z = 0 < / var> is the condition for maximization. Of course, everyday consumption activities are not done with mathematical optimal calculation. It is done intuitively.

Price effect and income effect

Based on the optimal consumption plan, if consumers decide the purchase amount, under the budget constraint, the purchase amount will increase as the price becomes lower. The price effect is that consumers' consumption decisions are influenced by price. When the budget constraint itself moves upward due to an increase in income, the purchase amount generally increases and the utility also increases. According to income, consumer's consumption decisions are affected as income effect. Even when assets increase rather than income as a flow, the amount to be spent for consumption increases, so the same effect as the income effect can be obtained. This is especially called asset effect.

price change and consumption

income effect

Current consumption and future consumption

In the optimal consumption plan, we consider the combination of the two goods that maximize utility, the purchase amount of A goods and B goods under the budget constraint, but consider the current consumption of A goods and B goods Considering it as future consumption, it is possible to calculate the optimal allocation ratio of present and future consumption. However, the future budget will be (1 + r) times the current budget.

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Judgment of consumption

In order to make purchase decisions of the various goods and services of the world, if the budget constraint also puts the monthly salary amount for one month as the total budget, furthermore if lifetime income of the lifetime is taken as the total budget, It can not be thought that the optimal solution is calculated by combining consumptions of various products / services that are countless in the head of consumers. Therefore, even if mathematical optimal solutions exist, it is considered that consumers' actual decision making is done by different values ​​and methods. Let us consider a model that simplifies the utility maximization problem under the budget constraint described above. Consumers think that they are judging that they will not buy a product by buying the utility and price that the product brings. Strictly speaking, consumers with assets and incomes, assets, consumers without income differ in view of prices. Even if I feel that prices are high if incomes increase, there are things to buy.

Therefore, introduce the parameter & theta; representing income / asset level. Utility values ​​are expressed as U = u _i (x) - px + & theta; . This is a model in which the utility value decreases when the price & theta; decreases if price p goes up. By appropriately setting the size of each parameter, consumption consumption to maximize U = u _i (x) - px + & theta;> 0 x < / var> intuitively, purchase, if any x becomes negative, it will abandon purchase.

Economic meaning of purchase

Let's think about what we are buying here. Purchase is the exchange of goods and money by sellers and buyers. The buyer hands the money to the seller and receives the goods instead. The seller receives the money and hands the goods. The seller and the buyer must be satisfied that the utility of both the seller and the buyer will be increased in order to make this exchange on their own will without being forced.

optimum consumption

Consumer characteristics

Preference for price

Consumers' preferences vary. For consumers and services offered by companies, one consumer puts high value, that is, to purchase at a high price, another consumer must purchase at a low price. Given income, when each utility function is a curve that gradually decreases with respect to the planned purchase quantity, since the purchase price is a linear increase function relative to the purchase amount, the maximum value exists. This is the purchase quantity. If the price rises, the purchase quantity will decrease. Rising prices reduce the purchase volume of one consumer, zero the purchase volume of another consumer, and leave the purchase volume of another consumer zero. Consumer preferences are diverse and purchase volumes vary, but price increases will reduce aggregate demand for the entire consumer. That is, the demand curve is a decreasing function.

Preference for time

Consider a case where utilities obtained from goods and services are obtained from different consumption on the time axis. For example, it is a combination of current consumption and future consumption. Even if the current consumption and the future consumption are fixed, the utility obtained from each consumer is different. Given total expenditure, future consumption will decrease if current consumption is increased. In other words, even though there is a temporal shift in consumption itself, decision of consumption should be made at the present moment. Determining the consumption plan from the utility obtained from the present consumption at the present time and the current utility derived from the future consumption.

One of the models that converts the temporal deviation into the utility value at the same time point is a concept of discount rate. This is to discount the utility obtained from the phenomenon ahead of time for the current utility by r (0 . For example, if utility U can be obtained after one period, it is set as rU if it is converted to utility at the present time. If U can be obtained after two periods, it is r ^{2 U} when it is corrected to the present time. In other words, the utility that occurs in the distant future will be smaller when converted to the utility of the present time. There are individual differences as to which of importance at the present time or consumption at the future is important, but this individual difference can be expressed by a difference in r value. People who place emphasis on presents more than the future r is small, and conversely, those who place emphasis on future consumption rather than current consumption r increases.

Preference for risk

Consider a case where the utility obtained from goods and services is uncertain. For example, if you do not know the value of goods or services beforehand, you know when you first buy it, purchase lottery, and investment you expected in the future return. Since the utility obtained in the future is not known at the present time, uncertainty necessarily accompanies it. It is only necessary to decide the future in the future, but there is uncertainty when asking for judgment at the present moment. Formulation of uncertainty is expressed using the concept of probability. Suppose that when purchasing product A, the probability of obtaining utility 100 is 0.7, when purchasing product B, the probability of obtaining utility 200 is 0.3. What kind of judgment will consumers make?

There is expectation utility hypothesis in what models consumer's preference for risk. Calculate the expected value of the utility obtained from the uncertain event, and select the one with the large expected value. In the case of the example, A is selected. The utility when x is obtained can be expressed as U (x) . x is an uncertain event and it is assumed that it follows a certain probability distribution. Note that the realization of x rather than computing the utility U (x) corresponding to the expected value of x It is to calculate the expected utility value by finding the utility of each value. Let's show by example. U (x) = 2x . x is an uncertain number with a probability of 0.5 and taking 1 with the probability of 0, 0.5. At this time, the probability of U (0) is also 0.5, and the probability of U (1) is also 0.5. Since U (0) = 0, U (1) = 2 , the expected utility value is 1. In another example, consider the case of U (x) = log (x + 1) . U (0) = 0, U (1) = log 2 . The expected value is log 2/2 . log (0.5 + 1) which substituted the expected value of x As shown in FIG. In general, in the case of the utility function having the property of diminishing the marginal utility, as the variance of the probability distribution increases, that is, the risk increases, the expected value of the utility decreases. Depending on the form of the utility function, the effect of reducing the utility value by risk varies, which appears as a difference in consumer's judgment on risk.

General form of consumer model

The utility that consumers obtain from goods and services is influenced by price, time and risk. In the case of continuous time, E [r ^{n {U (x) - px}} ] in the case of discrete time, > E [e ^{rt {U (x) - px}} ] .

Theory of demand curve

Demand is the amount consumers want to consume. It is the amount you want to consume, not necessarily the amount actually consumed. Given prices and how much you would like to buy for that price can be expressed as a function of price. This is called a demand function. The demand function can be thought of not only for one consumer but also for many consumer groups. From the viewpoint of selling products, when setting a price, it can be said that how much it can sell at that price is expressed by a function of price. Demand function is generally a curve that descends to the right with respect to price. It can be shown that it becomes a curve that descends to the right from the general form of the consumer model.

price elasticity

In the demand function, demand increases as prices rise and demand falls as prices go down. The degree of response of demand to price is called price elasticity. If the price changes by 1%, if the demand changes by x%, the price elasticity is x. Expressed as a formula, price elasticity = rate of change of demand (%) / change rate of price (%). The higher the price elasticity the better the product, the more consumers are sensitive to the price.

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Income elasticity and asset effect

Although calculation is similar to price elasticity, it is income elasticity that shows the degree of how demand changes with changes in consumer's income. Expressed as a formula, income elasticity = change rate of demand (%) / change rate of income (%). Goods with increased demand as consumer income increases are products with high income elasticity. It is common in jewelry and entertainment products. Those that do not correlate with income and demand of consumers are products with low income elasticity. It is common in food and daily necessities. Income is a flow of a certain period, but the increase and decrease of assets (real estate, stocks, financial assets, etc.) which are stocks also affect demand of goods like increase or decrease of income. This is especially called asset effect. If the asset value goes up, goods (luxury goods, jewelry etc) that demand increases due to the influence will be applicable.

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Producer's Theory

Scope of enterprise

When considering the simplicity of corporate activities, enterprise activities enter input elements (material purchase, product purchase), output elements (products, services) by capital (land, building, machinery equipment) It is said to produce. Considering the interface between the enterprise and the outside, "what to do" is replaced with "what to do in what range". This determines the business boundaries. This is the industry type. There are classifications of manufacturing industry and service industry, and there are classifications such as electrical equipment manufacturing, machine parts manufacturing, clothing manufacturing, construction etc. even in the manufacturing industry. More detailed, for example, in electrical equipment, it can be classified as audio equipment, health equipment, computer equipment and so on. Classification can be classified more finely if the category is finely divided. The narrower the scope of the company's business, the more concentrated it will be, the more competitive it will be, but because the market size will be smaller, the appropriate range will be selected. This is called the horizontal range. There are various processes to provide goods and services to consumers. In the manufacturing industry, it is the process of securing raw materials, parts manufacturing, final product assembly, distribution, sales, after-sales service. Distribution, sales and after-sales service are equivalent to service industry. An appropriate range is selected by choosing whether to process all the processes or to restrict it to some processes and to secure competitiveness through centralization. This is called the vertical range. For the scope of the company, you can see the size of the range with two rulers, horizontal and vertical.

Company objective

If the "what to do" is clarified, the company can do business. We must evaluate the results of doing business. What is done is "What", and performance depends on how you do it. The performance differs depending on the evaluation scale, so decide the evaluation scale. That will be the specific purpose of the company. The purpose of the company is the management function of the management. In general there are the following objectives.

1. Maximize the stock price (total value) of the company.
2. Maximize sales (market share).
3. Maximize profit.
4. Maximize employee welfare.

Modeling of corporate behavior

If you define an evaluation function, you can optimize by adjusting the decision variable. In the case of profit maximizing behavior, if the profit is π , then max π = (p - c) q - F , in the case of sales maximizing behavior, R max R = p q .

In general, management does not pursue only one purpose and sacrifice others. It is usual to think that you want to raise sales, raise profits, raise market share, raise stock prices, and raise reputation and reputation.

Environment surrounding the company

A company can not act alone. First of all, there is a supplier. There are destinations that introduce capital and labor for production and provide goods and services. The destination is usually a consumer or a downstream company. The company has other companies in the same industry. Compete with other companies in the same industry in the market. We will raise funds from the capital market to raise the necessary funds for the project. The labor force is procured from the labor market, and the enterprise and the outside are tied up by the market.

Corporate value

What should we measure if we want to evaluate the value of a company? One is the present value of the assets owned by the company. For example, it is factory, machine equipment, etc. Direct evaluation of assets is not the business itself of the enterprise itself but the resale value of only the physical assets used for the business. It does not mean you are evaluating the project itself. Factories, machinery and equipment, etc. are used as tools for doing business. The value generated by the project is the profit obtained by the project. If the profit is not transient and can be obtained over the future, the total value of future cash flows will be the corporate value. If future cash flows occur at different points in time, the discounted cash flow present value will be the corporate value in the future.

Production model

Production can be modeled by input and output. Production is a product, input is purchase, capital, labor. Y = F (K, L) F is called production function. The production function is modeled as a production method as a black box, but production depends on the degree of production technology even at the same input amount. Since F becomes an increasing function with respect to input capital and labor, output increases as you input it, but as a real problem, there are restrictions on input. One is budget constraint. To put in capital, capital borrowing fee r is required. Labor input costs wage w . In the budget constraint, r K + w L + f < I . Even if there is no budget constraint, the input amount is determined at the maximum point of the profit p Y - C = p F (K, L) - (r K + w L) - f . The condition for being a maximum point is p F '(K, L) = r p F' (K, L) = w The input amount is determined, and the output is determined as a result.

fixed cost, variable cost, marginal cost, average cost

Costs can be divided according to their nature as follows. Costs vary with production volume and others vary with time axis. The cost that changes according to the production volume is the variable cost. Raw material costs, utility bills, etc. Regardless of production volume, such cost is fixed cost. Personnel expenses, administrative expenses, advertising expenses, research and development expenses, etc. In the short term, fixed costs may change in the long term. Separate fixed costs and variable costs depending on whether you watch in a short term or long term and what is fixed against what you are fixing. For a certain amount of production, additional costs necessary for additional production of one more is also called marginal cost. When producing a certain number of production, the cost (fixed cost and variable cost) required for production is divided by the number of productions and is called the average cost (cost per production).

opportunity cost, sunk cost

There is expenses to spend on doing business before production. For example, it is an initial cost such as plant construction and capital investment. Since these are done before production, they are fixed at a fixed cost to the production volume and have been expended in time. This cost is called a thunk cost, and it can not become a decision-making target at the time after payment. Decision making after payment is determined regardless of the size of the sunk cost. Another point of view is opportunity cost. Opportunity cost refers to the return amount obtained when a certain fund is used for another purpose (usually the best quality project among different objectives). By using funds for the original purpose, you will not get the return you get if used for a different purpose. This is opportunity cost. In general, the opportunity cost for investment projects is the amount of interest that would have been obtained by depositing investment funds in financial institutions. If the alternative to the investment case is stock investment, the return of the stock will be the opportunity cost. Since investment, stock investment, and deposit are different in risk, it is not possible to simply compare the amount of return alone. Comparing expected values ​​alone is not enough. Deposits have low returns but low risk. When risks are found for investment projects and alternative projects, they are compared by utility value. The opportunity cost of the investment case is the expected value of the project with the highest utility value other than the investment case.

Production problem

To maximize profits, there are two ways to maximize production at constant cost or minimize cost with constant production volume. Formulation of the problem of production will be as follows. F ₂ (k _{2, /} L2)], k1 + k2 = K, L1 + L2 = L max p F (K, L), r K + w L + f = I min [r K + w L], F (K, L) = Y Each of them is a problem of constrained optimization.

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Break-even point analysis

Break-even point analysis is a representation of the relationship between cost and sales. In the break-even point analysis, by checking the market price of the cost necessary for production, it is indicated whether or not it is not surplus unless at least some sales are made. Since it is planning the business to produce a surplus normally, it helps to set the scale of business and sales targets. Expressed in formulas, the breakeven point is obtained from pq = aq + b q = b / (p - a) . Transfer this formula, on the contrary, selling price, p = a + b / q If you do, the balance will be zero. To obtain a certain profit g , the breakeven point is q = (b + g) from g = (p - a) q - b / (p - a) .

As a cost to do business, it is divided into fixed cost and variable cost, and it shows how much sales can be recovered if sales are available. The point where the profit is zero is called a breakeven point. Generally, employee's wages, office rents, etc. will not change even when sales of products change. This is called fixed cost. On the other hand, purchasing expenses, material costs, utilities costs, transportation expenses, etc., make more products, the more they sell, the more expensive it costs. This is called variable cost. If the cost of producing and selling one item is constant, the following relationship holds. TVC : variable cost, VC : Variable cost per unit, Q : It is the production sales volume. Together, variable cost and fixed cost will be the total cost. TC = TVC + FC = VC Q + FC where TC : total cost, FC : fixed cost . Since the sales are S = PQ ( S : sales, P : price), at the breakeven point, S = TC and Q where PQ = VC Q + FC holds. Although you can tell by drawing a graph, the break-even point, which is the sales amount that collects expenses, varies with fixed costs, variable costs per unit, price. The straight line which translated the straight line of the total cost up is the equal profit line. It shows the income (sales) necessary to obtain a certain profit. The intersection of the equal profit line and the sales line is the production sales volume with a given profit. Break-even point analysis helps you to see if profit or investment can be recovered if income and expenditures change, depending on production volume. How can I make a profit? As you can see from the figure, you can reduce the fixed cost, reduce the variable cost per piece, increase the price, but actually it is not easy. There is a possibility that sales volume will go down if price is raised. Variable costs may increase as a result of lower fixed costs. However, if each value changes, you can see how the breakeven point changes. The ratio between the actual sales volume and the break-even point sales volume is called the breakeven point ratio, which is an index representing the margin of sales.

Cost Analysis

In the break-even point analysis, we assumed that variable cost per piece is constant with respect to production sales volume. Let's relax this assumption and assume that the variable cost per unit changes with respect to production sales volume. Since variable cost is originally variable cost, variable cost varies with production sales amount, but note that variable cost per unit changes. In the break-even point analysis, sales are placed on the vertical axis, but here, the price per piece (price or cost per piece) is placed. Putting constant variable cost per piece. It becomes a horizontal line. The price is also a horizontal line. Since the total cost is TC = TVC + FC = VC Q + FC , the cost per unit obtained by dividing the total cost by the sales volume (average cost) is AC = TC / Q = VC + FC / Q . Notice in the figure is the average cost curve. Due to the influence of such fixed costs irrespective of production sales volume, the average cost decreases with increasing production volume and approaches the marginal cost curve. Decrease in cost per unit as production volume is called scale economy. Companies that produce and sell more are able to sell at a lower price than other companies or if they have the same price as other companies, they can make more profits. This effect becomes more prominent as the fixed cost increases. In general, the higher the price the lower the demand, the lower the price the more demand. Put the demand curve in the plane of quantity and price of the figure. It falls to the right from the nature of demand. If you sell at a price above the average cost curve you will get a profit. However, it can not be sold without demand. Assuming that we produce and sell for the demanded amount, the distance between the demand curve and the average cost curve is the profit. If you produce and sell for the demand, the price will be a function of production sales volume. R = PQ - TC = f (Q) Q - (VC Q + FC) . In order to maximize the profit by changing the production sales amount, differentiate the profit formula with the production sales amount and set it to zero. f '(Q) Q + f (Q) - VC = 0 Q satisfying this expression is the condition of the local maximum value. (Strictly speaking, in order for this to be the maximum value, it is necessary that one value satisfying the condition is one and the change before and after it maximizes the profit formula.)

Supply function

The production plan that maximizes the profit of the company is max [pq - TC (q)] . If the marginal cost is constant at m , then max [pq - (mq + F)] = max [(p - m) q - F)] When the market price p is given, if you produce indefinitely for p> m you will gain indefinitely. Since p produces a loss as much as it produces, it is a choice not to produce. In reality, it is natural to think that the marginal cost as well as the fixed cost rise as it tries to produce in large quantities. Thus, given p given max [pq - TC (q)] there is a finite optimal value q . Total of q of each company is the production volume of the entire market. The aggregate production amount becomes a function of rising upward with respect to price.

Economy

Manufacturing involves various technical factors. R & D expenses, advertising expenses, operating expenses, administrative expenses are fixed costs, and labor costs of manufacturing departments are also fixed costs in the short term. The production cost per one is AC = TC / Q = VC + FC / Q , and the existence of fixed costs is lower the cost per unit the larger the production cost. If you mass-produce a large volume from a competitor, you can earn a bigger profit than competitors, or selling it a bit cheaply will be advantageous for competition. This is called the economic effect of the scale. In recent technological innovation, the proportion of fixed expenses such as R & D expenditures is larger than variable expenses, and the production scale is increasingly deciding competitive power in market competition. Rather than producing a single product, producing two products may lower production costs. The reason is that there are many common parts in the technology and production process used in the two products, and it is possible to produce more efficiently by simultaneously producing the two. Secondly, if there is a common part in raw materials, it is possible to lower the procurement price by mass purchase. If the production cost of the original product decreases by expanding the range of production, this is said to have a range economic effect. Computer products etc., use various units connected together. Products that are designed according to industry standards at that time are good for connectivity. Among products of various standards, those that are produced and sold in large quantities are attracted to consumers. This brings further market share expansion. This property is called network externality. Producing in large quantities is another advantage in terms of cost. In the process of accumulating experience of production, learning effect is generated by efficiency improvement, optimal placement, quality control etc. of production department. By learning production, cheaper and higher quality products can be produced. Producing in large quantities and producing in a wide range is a matter of cost and competitiveness of products in the competition with other companies.

Scale economy

Expenses not related to production quantity: The existence of fixed costs shows the economic effect of the scale that the production cost per one decreases as the production quantity increases. If the production cost per piece is reduced, the price in the market can be reduced and the market competitiveness can be increased. On the contrary, producers who can not make use of the economic effects of the scale can not raise profits in the market and forced to leave. Assuming that the number of production is q, variable cost (per unit) m, fixed cost is F, production cost per unit = m + F / q. The larger the mass production, the lower the price can be set. In the industry with large fixed costs such as production facilities and R & D expenditure (heavy machinery industry, high-tech industry), the economic effect of the scale is large, giving the grounds that a very large number of large enterprises are mass-produced massively. In the industries that require large production facilities and industries that require research and development costs, for example, in the automobile, electrical machinery, machinery, and medicine fields, the economies of scale are highly effective, so that few companies compete in the market.

economy of scope

Expanding the scope (type) of production reduces the production cost per one (type), the economy of scope. If you compare the case of producing one thing and the case of producing two things and if the cost of producing two things is less than twice the cost of producing one thing, It means that there is an economy of. Generally, if there is a common part in terms of R & D, production equipment, labor input in the production of multiple items, there is economic effect in the range. In this case, expansion of product lineup and diversification of business will enhance competitiveness. Also, not only the type of production but also the case where it is economical to carry out a wider range of processes than carrying out only a certain process from the upstream process to the downstream process.

economy of consolidation

With a similar concept of economy of scope, it is better to combine the production of a business, the production of goods, and the production of services than to combine multiple businesses by synergistic effect, rather than doing a business independently. Effect. By offering to consumers at the same time combinations of products and services that do not have commonality, it is possible to provide higher value (than the total value provided alone), to provide higher price, If the effect of increasing market competitiveness is obtained, the economic effect of consolidation exists. A representative example is the IT industry. By combining hardware and software, content, and net service, it is possible to create higher value.

Network externalities

In the IT industry, functions and performance are demonstrated by combining hardware, peripherals, software, and the like. It is a prerequisite to combine. In this case, ease of connection enhances the value of the product. Industrial products have various standards, but products conforming to standards with high market share are highly connective. If products of that standard are popular, products easy to connect with the products are easy to select. For this reason, not only the original functional performance of the product but also the popular and high market share is the appeal of the product, and in many cases the spread and share are accelerated. This is called an external effect of the network (connectivity) (an effect other than the original functional performance possessed by the product), and it is a concept that is emphasized in advanced industrial fields such as IT.

Market Theory

Market structure

You will go intuitively and feel that cheaper one buys the price of certain goods will happen. Whether to buy or not depends on your value attached to the item. To buy at 10,000 yen is because you are going to respond with exchange of that product and 10,000 yen, because it worth more than 10,000 yen for that product. Because it specializes by exchanging things and money, it responds to the exchange. However, the value attached to that product varies from person to person. Therefore, the judgment that you will not buy will be individual for each price. However, the price has never been cheap, so the more cheap the price, the more people want to buy. Given the price, it is the demand function that expresses how much buyer gets as a function. However, since the demand function shows the correspondence relation that it can sell ○ ○ if it is ○ ○ yen, in order not to actually experiment (actually sell) in various price ranges, I do not know the form of the function. In general, however, it is natural to think that the higher the price, the more it will not be sold. On the other hand, from the supply side, in order to sell all the products produced, it is necessary to set a market price determined by the demand function.

Supply curve

If the price changes according to the price and it becomes the demand curve, that is the same on the supply side. In general, the supply curve rises to the right, that is, as the price rises, the amount you want to sell increases. Why does the price rise, the producer side increases the amount you want to sell? There are two reasons. One is that the higher the market price for the production cost, the higher the profit, the more companies entering the business, producing and selling. If there are variations in the company's production costs, the higher the market price, the more companies will be in surplus and the overall production volume will increase. Another is the idea of ​​optimum production volume. Considering one company, as the production increases, the marginal cost (additional expenses if one production is increased) will increase, so given the market price given, the optimum production volume is determined, The summed up value will be supplied to the market. Optimum production is a function of price, the price increases, the optimum value also increases.

Demand Curve

If it is the same item, the price should be cheaper. Purchases are refrained as prices become higher. Every consumer can not affect the price. Thus, given a price, the amount of purchase will be a function of price and will be on the right side for price.

Supply and demand

The relationship between producer and consumer is in the relationship between seller and buyer. On the other hand, if consumers are earning income as workers, they are sellers of labor services and buyers are companies. In the case of real estate trading, equity investment, bond investment, they become sellers or buyers by trading. In the case of loans, the lender is the buyer of funds borrowed by the seller of funds. However, the conditions for establishing a transaction vary from case to case. In the case of producers and consumers, the consumer's judgment is utility value, but producer

Aggregate demand and aggregate supply

In a market where there are many producers and many consumers, the supply-demand relationship is determined by the aggregate demand function and the aggregate supply function, and the price and the transaction volume are determined. Practice the demand curve and supply curve with production sales on the horizontal axis and price on the vertical axis. The intersection of the demand curve and the supply curve (price, transaction volume) is a transaction realized. It is only observable that intersections (price, transaction volume) are realized values. The figure depicts a simplified demand curve and supply curve. If demand increases for some reason, the demand curve moves to the right and the intersection also moves. As a result, both price and transaction volume increase. If demand falls, both price and transaction volume will decrease. On the other hand, when the production cost of raw materials, personnel expenses, etc. declines, more products are produced even if the given price is the same. The supply curve moves to the right. As a result, the price decreases and the transaction volume increases. When the production cost rises, the price rises and the transaction volume decreases.

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Form of competition

The form of market competition is mainly the following three. There are producers and consumers, but it is assumed that there are an indefinite number of consumers.

Complete competitive market

It is a market that assumes that there are an unspecified number of producers. Individual producers and consumers are small ones, and it is a market that does not affect the price at which individual production consumption behavior is formed in the market. Food and agricultural markets are representative. Each producer consumer calculates the utility value, the profit given the price, and takes the optimized action (production amount, consumption).

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oligopoly / monopoly market

A small number of producers is a market that influences price fluctuations due to the influence of supply-demand relations in decision making of individual producers. Typical examples are durable consumer goods market, electricity market. Consumers act with given price given, but producers can act to maximize their profits, and producer side benefits.

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Monopolistic competitive market

Although the number of producers is large, the products of individual producers have their own specifications, functions, designs, and consumers are markets that can not select products by simply comparing price alone. As products are differentiated, for consumers who prefer a specific product, the number of producers supplying that product will be a small number (or one company), so the behavior of producers will have a major impact on price formation give. This is the current durable consumer goods market.

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Competitive market comparison

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Marginal cost pricing

The marginal cost is the additional cost when one piece is additionally produced. In the above example, although the marginal cost is assumed to be constant, in general, the marginal cost decreases, such as learning effect and bulk purchase of raw materials as the production amount increases, and when the production exceeds a certain production amount, the marginal cost rises Begin to. As long as "production price> marginal cost" is satisfied, if you increase production, additional profit "price - marginal cost" will occur, so increase production. As we continue to increase, the price decreases due to the nature of the demand curve and the marginal cost increases. When "Price

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Average cost pricing

With marginal cost pricing, there was no fixed cost consideration. Marginal cost pricing represents the most profitable state, but does not guarantee that it is a positive value. In other words, it does not change to the best condition, but it may be the state with the least loss. To see whether positive profits are included including fixed costs, that is, see if all expenses are being collected, look in relation to the average cost. The average cost is the one that fixes all costs including one fixed cost per one. If "price> average cost", all costs are recovered and profits are given out. If the scale economy works, the average cost will decline if production increases. However, the decline will become gentle as production increases. On the other hand, if the production volume rises the price that demands it will fall. If production increases, profits will continue to appear during "price> average cost" but eventually there will be no profit when "price < average cost", so we will not produce it. Therefore, since the profit is zero for the production amount "price = average cost", it will settle somewhere in "price > average cost". The point of "price = average cost" is lower than the point of "price = marginal cost".

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Entry and exit

Suppose one company enters when n company is competing in the market. If any company is targeted and has similar technical and productive capabilities, it is expected that the profit per company will be reduced if becoming n + 1 company. The reason is that the total production volume of each company will not change unless demand changes, the production volume per company will decrease. Or if the production volume per company is maintained, the market price decreases as the total production volume increases, and the profit per company falls. In either case it will lower profit. So why do not we enter a state of equilibrium without entry or exit under any conditions? Conceptually, in the case of equilibrium with n companies, R (n - 1)> 0 , R (n) = 0 , R + 1) <0 holds. This is a case where each company is targeted, and if there is a difference in technology and productivity of each company, companies with high productivity succeed and enterprises with low productivity are forced to leave. This replacement brings about an increase in industrial productivity. In markets where economies of scale are working, companies with large market share are advantageous, and companies with small share will exit. In this process, the number of companies making up the market will decline, and in the end the market will be constituted only by a few companies. It is the process of oligopolization. Entry into the enterprise will not take place unless it is expected that profit will come out when entering the market. Current situation, there are situations where entry does not occur even if R (n - 1)> 0 . This is called entry barriers. Entry barriers include the following.

1. Markets where economies of scale are working. Entry companies are unlikely to raise profits unless there is a prospect of mass production sales.
2. Market with high initial cost. When entering into business and starting a business, if the initial cost incurred at the start of business is high, fund procurement and collection of funds become a problem and can not enter.
3. Market with reserve capacity in existing companies. Even if it is anticipated that there is sufficient victory by analyzing the present situation, if it is anticipated that new product introduction, price reduction, production volume competition, etc. are anticipated as a countermeasure to entry, unless profit is expected in the competitive state after entering , Entry does not occur.

Market life cycle

In modern industries, a small number of companies often form an oligopolistic market. The life cycle of the industry is as follows. When a new market (industrial) is born, the market size is small, and many entries into new markets occur in search of business opportunities. The number of companies competing in the market increases as the market size increases. Eventually, competition will cause differences between companies in technology and productivity, competitive companies will gain market share, and companies with no competition will leave the market. Companies that are seeking new entrants will not participate unless the prospects for profit are high by competition with existing companies. Therefore, the increase in the number of companies stops. In markets where effects such as economies of scale, economies of scope, external network characteristics work, companies that are obliged to leave when there is a difference in market share will emerge. When the market matures and market size does not grow, the number of enterprises declines, and when the economic effect of the size of existing enterprises becomes to work due to the decrease in the number of enterprises, the market is stable and an oligopolistic market is formed.

Competitive strategy

Production volume competition

To anticipate the production level of competitors and to decide their production volume so that their profits are maximized under that condition. Everyone participating in the market will compete in production if you decide the production volume of your company like this. The motivation to raise the production amount is that various benefits such as the economic effect of the scale, the acquisition of the position of the industry standard, the learning effect and the like, in addition to the view that the profit will increase if the market price is somewhat lowered Yes, and often it can result that each company falls into overproduction, lowering the profit level of the industry as a whole.

Price competition

If you compete in the market with homogeneous goods, you can earn a large share only by presenting cheaper (just a little cheaper) price than other companies. As each company competes with just a little cheaper price than other companies, the price calms down at the level that matches the production cost theoretically. Writing competition is profitable for consumers, but for producers, there is a situation where profits can not be made.

Product differentiation competition

In order not to fall into production competition, price competition, not to compete with homogeneous goods. In homogeneous goods, the market price of its own products is affected by the production volume of other companies, or it is involved in price competition by discounts of other companies. A strategy that avoids the influence from other company products by differentiating products, differentiating functions, performance and design is effective for securing certain profits. However, you can not gain a big profit by gaining market share across the market.

Competition for customer segmentation

It is a concept similar to product differentiation, and we introduce products targeting only specific consumers to the market. In this case, if a specific target consumer is separated from other companies, it has the same effect as product differentiation.

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Game Theory

It is a mathematical theory to analyze what kind of decision will be realized when multiple decision makers make their own decisions by incorporating competitor 's decision making. If we decide to maximize profit, it will be useful for analysis of decision making of various economic entities competing in the market. Since it is a theoretical analysis, it is a discussion on the premise that all economic agents take reasonable action (profit maximization behavior). In typical analyzes, companies' decision making (oligopolistic market) (production volume, pricing, investment amount), the Nash equilibrium (when each decision makes a decision, the profit maximization behavior was taken as a result Decision making to be realized). In the analysis theory of game theory, in general, individual decision-makers maximize the total gross profit (the sum of the profits each individual decision-making entity obtains) by acting by considering only maximizing their own profit It is said to balance to an inefficient state.

Nash equilibrium

Participants in the game think that each wishes to predict the participants of others participating in the game and to select a seller who maximizes their own interests. In this case, you can not decide who you are unless you have confirmed the owner of another person. In other words, you can not win unless you are a late scoosh of scissors. Since all the participants in the game think so, the game itself does not hold. However, when considering all the combinations of the speakers of each participant, when there is a combination of speakers that satisfies the following conditions, the game is established by actually selecting that speaker. Explain in the case of two parties.

• If you assume that the partner's taker is S2 , the vendor that you get the most benefit is S1 .
• If you assume that your vendor is S1 , the partner's most profitable vendor is S2 .

If there are combinations of S1 and S2 that satisfy these two conditions, this state is called Nash equilibrium and becomes the player of the game.

Bilateral competition

In competition research, bilateral competition is the simplest as a model and is used for analysis of various competitive forms. We introduce some models. Nash equilibrium: When similar companies are competing in the market, they read their opponent's strategy and decide their own strategy under that condition, and the other company is in Nash equilibrium when it is similar.

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Strategic substitution and strategic complementarity

If the other company decides to make decisions on the premise when the production volume expands, take action against the opponent when production reduction becomes the optimum reaction. This is said to be a strategic alternative. Production volume competition is applicable. When the opponent company lowers the price, assuming that, if the price reduction is the optimum reaction itself, it follows the action of the opponent. This is said to be a strategic complementary relationship. Price competition is applicable. If the partner company is big and has market control, he will take the action of the opponent and will take the best action on that assumption. Meanwhile, large partner companies are not affected by their actions.

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Two-stage game

Game theory in the case where decision making of two or more economic agents is carried out in two stages. For example, in the manufacturing industry, research and development of manufacturing technology is carried out as the first stage, products are produced and introduced to the market by the developed manufacturing technology. Assuming production competition is to be done in the market, decision making of each company's production volume is a game. If the production volume of each company is decided, on the basis of this, the R & D investment amount is determined so that the net income minus R & D cost is the maximum from the profits obtained in production. Decision making (production volume and research and development investment) has two stages, and each stage is decided by incorporating decisions of competitors. What is distinctive is that, contrary to the time flow of research and development, then production, production decision making, then R & D decision making is done.

Repetition Game

It is a game that analyzed the case where decision by game is repeated many times. In a game that is repeated indefinitely, results are different from finite times games. In the game of the finite floor, the decision is made in order from the last phase. On the premise of making decisions to be made in the last game, it is decided to finally decide the first decision by back calculation, such as the previous decision making and the previous decision making. On the other hand, in infinite repeating games, there is not final decision making, so we can not backward calculate decision making each time. In this case, cooperative decision making that does not happen in ordinary games may be realized in some cases.

Social welfare

Economics is a discipline that expresses economic activity with price and quantity and analyzes it. It depicts the mechanism hidden in economic activity and does not judge the value whether its economic activity is good or not. Since judgment of value of things such as good and bad is each person, it can not be stepped in economics as well. However, for a certain part, we can evaluate the value of economic activity (good situation or bad situation) with a measure called social welfare.

Public goods

We can categorize various kinds of products and services people use.

• Can not restrict users / Restrict users
• No restriction on the number of users / Limitation on the number of users required

If the user can be restricted, the enterprise can collect usage fee (purchase price) from the person who wishes to use, and establish the business of providing goods and services as a business. Conversely, if users can not be restricted (that is, in a state where unspecified number of users can freely use), it is impossible to collect usage fee (purchase price) and does not become business. Nevertheless, if it is necessary for an unspecified majority, it will be supplied by the government. When the number of users is limited, the number of users can not be controlled unless an appropriate fee setting is made. Because it can not provide free of charge, it is suitable for business. On the other hand, if the number of users is not limited, it can be provided free of charge. Things that "can not restrict users" or "no limit to the number of users" in goods or services are called public goods, and are normally provided free of charge for unspecified majority. Well-known examples are parks, police, lighthouse, etc.

Public economics

Economics is mainly the analysis of production of goods and services performed by private enterprises, but it is an academy to analyze the goods and services offered by the government using analysis methods cultivated through the analysis . Public goods provided by the government, benefits of public works projects, economic policy, taxes to be funded, etc. are analyzed.

Externality

In the case of economic transactions, if the effect of the transaction exceeds the parties concerned, it is said to have externalities. Examples of externality are pollution problems, garbage problems, resource waste problems, and so on. When producers and consumers trade on the market (purchasing products), byproducts of production (exhaust, drainage, waste) are not sold to consumers. It is only thrown into the environment, its costs are not borne by both producers and consumers. However, it becomes the cost of society as a whole as pollution. As neither producers nor consumers will bear the cost, there is no incentive to control pollution, so the cost of society as a whole will not be restrained.

Government's Role

In the case of an economy in which externalities exist, even economic activities that constitute the cost of society as a whole are left uncontrolled without being burdened by the parties (producers and consumers). Therefore, government involvement is necessary. As means of involvement, (1) regulation: make it impossible to produce without adding pollution eliminator. Increase in production cost in this case will be converted to consumer (2) Taxation system: taxes on production and consumption, controlling production (pollution accompanying it). We will take measures against pollution with collected taxes.

Personal interest and social benefit

The occurrence of externalities indicates that the interests of individuals and the interests of society do not match. Even if pursuing the interests of individuals, if the cost of society arises as a result thereof, it will eventually have a negative influence on the individual's profit and lower the profit of the individual. Rather, it may be the benefit of individuals as a result of suppressing the pursuit of individual interest so that social costs do not occur. Here is the role of the government, which controls economic activity through economic policy and regulation.

Consumer surplus

The transaction established in the market is the intersection of the demand curve and the supply curve. Since the consumer demand curve is downwardly inclined to the right in the price quantity plane, there is some demand even for prices above the intersection market price. The utility against goods varies from consumer to consumer, and for some consumers who are willing to purchase at prices above the market price, they will be able to purchase items cheaper than the value they think. It is said that there is a benefit of consumers to receive this benefit (if a consumer who thinks that it is worth 10,000 yen can actually purchase at a market price of 7000 yen, there will be a benefit of 3000 yen). By integrating the benefits received by each consumer, the benefits received by the entire consumer can be calculated. The way of calculation is shown in the figure. Consumer surplus is the benefit that the entire consumer receives. In the figure, the consumer surplus is the area of ​​the portion between the horizontal line passing through the market price and the demand curve.

Producer surplus

Benefits are also on the producer side. You can profit by selling it to consumers. In the equation, (p - c) q is the profit, which is the shaded part in the figure. The profit is the benefit that the producer receives as it is, and it is called the producer surplus.

Social welfare

In market transactions, consumers receive benefits by differences between the utility and expenses of goods by exchanging their money and goods. By receiving money in exchange for goods, the producer receives only the difference between the receipt price and the cost (purchase, production cost, etc.). The total benefit of market transactions is the sum of consumer surplus and producer surplus. When discussing a desirable market form for society as a whole, it is helpful how this social welfare value changes.

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Pareto optimal

If the social welfare value rises, it can be said that it became better than the previous state. This state is the best condition socially in a state where the social welfare value does not increase any more even if market prices and transaction volumes change. In general, in a market composed of multiple stakeholders, if there is room to improve the benefits of all members, it can be said that the current state is not optimal for the entire market. On the other hand, Pareto optimal state can not improve the benefit of another someone without lowering the benefit of someone of the stakeholders. Pareto optimal means a case where there is no clearly better condition (a state that improves the benefits of all members) besides this state. Economically, the Pareto optimal state is defined as the most efficient state.

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Individual Optimization and Overall Optimization

Participants in economic activities are composed of various economic agents such as consumers, producers, financial institutions, and governments. With a free economic system, each economic entity makes decisions, but it is assumed to basically act to maximize their benefits, except for the government. This is decentralized decision-making. Making separate decisions based on individual interests rather than overall profit by each entity does not guarantee that the overall profit is maximized. Overall profit is assessed by social welfare value, but there is a possibility that it will not be Pareto optimal which is not maximized. Once formulated, each economic entity maximizes max [v (x)] and max [v (x ₁ ) + Since we do not maximize v (x ₂ ) + v (x ₃ ) , the benefits society as a whole do not benefit It will be sufficient. In terms of economic efficiency, centralized decision making max [v (x ₁ ) + v (x ₂ ) + v (x ₃ )] may improve not only the overall benefit but also the benefits of any economic entity.

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Economics of uncertainty and risk

Uncertainty and risk

When it is uncertain what happens about the future, it says there is uncertainty. Economic activity is also uncertain about the future. Uncertainty does not apply to mathematical modeling and it is not subject to analysis even in economics. On the other hand, there is a risk in the same concept as uncertainty. Although there are various risks, it is possible to analyze risks that can be modeled. The risk that can be modeled is the event (event) that is likely to occur even if you do not know what will happen, and you know the frequency of occurrence of each event individually. In this case, it can be analyzed using probability theory.

Modeling of risk

Uncertainty means the case where the future is unknown, and can not be formulated in the first place. Risk management does not make unknown things unknown, but extracts what is known even in uncertain circumstances and puts unknown ones into formal expression so that it is subject to management . Uncertainty can be formulated by listing all possible events and considering the occurrence frequency of each event. For example, we write down all possible events with the expression "an event of A occurs once a year," the event "B occurs twice a year", and the frequency Which is to be determined. Frequency, of course, is not clear as it is the future, but usually we assume frequency by the following method. (1) If all potential events are N and can occur in the same way, the frequency of occurrence of one event is assumed to be 1 / N . (2) In the past data analysis, if N occurred in M occurrences, the occurrence frequency is N / M < /var>.

Risk in corporate profits

For example, formulate a company's future profit forecast. Make the profit amount an uncertain event. Possible event candidates are represented by numbers such as -100, -50, 0, 30, and 150. If probabilities are given to each candidate, a probability density distribution with the profit amount as a random variable can be created . From the probability density distribution, it is possible to calculate the expected value and the standard deviation (risk) of the random variables, and by using these two statistical values, the nature of uncertainty can be expressed to some extent. The shape of the probability density distribution varies, but if it is approximated to a certain pattern, mathematical calculation becomes easier. Prediction of economic activity differs from physical science such as precision science, so it is safe to replace it with a handy distribution pattern in practice. Practical patterns are normal distribution, uniform distribution, triangular distribution. Since the shape of the distribution is uniquely determined by determining expected values ​​and standard deviations, assuming the above distribution, after that, analyzing only the expectation value and standard deviation (risk) of the nature of uncertainty it can.

Investment risk

Investment is risky. After making investment and carrying out business activities such as production and sales, sales proceeds are collected, but due to the time difference, investment decisions will be made by anticipating future returns. Although the future is uncertain, formulate this uncertainty with a probabilistic model. Let X be a random variable representing return. Future returns may take various realizations such as X = 0, X = 1, X = 2, X = -1, X = -2 If a certain investment case A has a probability that the return becomes 1, it is expressed as P (X = 1) = 1/3 . Likewise, the risk of this investment case A is expressed as P (X = -2) = 1/6, P (X = -1) = 1/6, P (X = 0) = 1 / (X = 1) = 1/3, P (X = 2) = 1/6 . P (X = 0) = 1/6, P (X = 0) = 1/6, the risk of another investment case B under consideration is P (X = , P (X = 1) = 1/3, P (X = 4) = 1/6 . The expected value of future returns is the sum of the realized value multiplied by its probability, and the two investment cases have the same expected value when calculated. If the expected values ​​are the same, are the two investment projects the same? However, when calculating the standard deviation, it can be said that B has a larger value than A, and B has a higher risk.

Expected utility hypothesis

In the probabilistic world, there are probability distribution, expectation value, standard deviation as the property of random variables. Economic activity is a human activity, and evaluation on risk is also subjective. Evaluation and evaluation are also subjective in future results. The degree of satisfaction that a certain circumstance brings to a person making a decision is called a utility. Even if you get 100 utility when you get a return of 100, the utility when 200 returns are not limited to 200. On the other hand, when the return is -100, the utility is not necessarily -100, and in some cases it is felt as -200. Therefore, the utility function graphs the utility value (satisfaction level) for each value of return. The figure shows three kinds of utility functions. If the return is probabilistic, corresponding utility is obtained for each realization value, which is also probabilistic. The expected value of the utility obtained from the two investment cases is the expected value of U (X) , where utility function is U (X) . The point to note here is that the expected value of U (X) is the expected value of utility, not utility corresponding to the expected value of X is there. Three utility functions are shown, each of which is called risk averse, risk neutral, risk appetite. In general, risk is avoided. A negative return is recognized as being greater than a positive return. Even if the return gets bigger, the utility does not increase to the extent of the increase. If investors are risk-averse, even those with the same expected value, the smaller standard deviation is preferred.

Risk preference behavior and risk avoidance behavior

What actions should be taken when an economic entity is aware of risk? It is the market world that you can see actions against risk immediately and directly. Risk in the economy refers to a situation where the results of future profits and losses are unknown now. Currently we will anticipate and act even if the future is not finalized. Even if it is supposed to cause a major loss, if it knows "the result of profit and loss", it does not fall under risk. There is always a return, in case you will lose without fail, you will not get lost your judgment. The subjects of risk are the options that the return is large but the loss is large, and there is the option that the return is small but the loss is small. It can be interpreted that the risk is higher as the result variation becomes larger. The risk object is defined as a random variable, the future profit and loss is defined as realized value, and the degree of variance of realized value is defined by standard deviation. Risk aversion is to move behavior from a high risk state to a low risk state. In other words, converting the risk assets that seems to have a high standard deviation to the form of assets that the standard deviation is expected to be low. Here, the expression "it seems that the standard deviation is high (low)" is not that the probability distribution and the standard deviation are not given as in the natural science phenomenon or the expectation of the eyes of the dice, It is based on the selfish prediction of the house. In general, risk avoidance behavior of investors is done in the following order. This is in the order of stock → bond → cash (foreign currency) → cash (home currency). In risk avoidance behavior, investment shifts from a high standard deviation state to a low standard state.

Liquidity preference

Consider an example. Suppose that "stocks will fluctuate widely against cash in the future". On the contrary, "Cash fluctuates greatly with stocks". The value of currency is not absolute, it can be inflationary and deflation against thing. The change in value is relative. Stocks are exchanged for cash, but cash can be exchanged for almost all goods and services, not just stocks. Since the goods and services to be exchanged are infinite, even if the exchange ratio with individual goods and services fluctuates, the average exchange ratio changes only slowly. The standard deviation of the value of cash, measured in exchange ratio, for goods and services can be said to be less than the standard deviation of the value of shares that can only be exchanged for cash. The property that there are many replacement items or that they can be replaced immediately is called liquidity. As risk increases, it shifts from low liquidity to high liquidity. Previously, at the time of the subprime crisis in the US, there were many buyers even though there were many subprime securities vendors, there was a case that the deal did not go through and the price could not be reached. This means that subprime securities can not be replaced at all in emergencies. There is no fluidity. Since there is no actual measurement, even when a buyer of subprime securities appears in the future, the exchange ratio can not be determined. The price (value) of subprime securities will be indeterminate.

Liquidity is determined according to individual risk assets, and there is no individual difference. On the other hand, individual differences arise about the standard deviation of the value of risk assets. For example, if you live in the United States, the standard deviation of the asset value will be smaller than the one with the dollar as the asset as the asset value. People living in the United States need dollars to purchase goods and services. In the case of holding in yen assets, we will purchase goods and services once we convert yen into dollars. Since the exchange rate between yen and dollar will change, if you look at the currency value with the purchasing power of goods and services in the United States, the dollar has a lower risk. On the other hand, for those living in Japan, the yen becomes lower risk, and as risk avoidance behavior, we take action to exchange dollar assets we own with yen assets. In this way, the degree of risk of assets is different between economic agents and investment entities, and when risk avoidance each individual acts to become a state of low risk to each subject.

Decision-making under risk

Suppose there are risky investment projects A and B. Plot the standard deviation (risk) on the horizontal axis and the expected value on the vertical axis and look at the plot of the investment cases A and B. If the expected values ​​are the same, the smaller standard deviation is preferred. If the standard deviations (risks) are the same, the one with the larger expected value is preferred. That is, in the figure, the item in the upper left direction is preferred. Even though it is risk-averse, it is natural to think that the utility function of each investor has individual differences, but it is common that better upper left is better than lower right. Plot the points that gains the same utility gathered as the equal utility line. Although the shape of the curve varies depending on the utility function, consider it as a straight line. If you write a few equal utility lines, you can see which investment projects are better.

Investment and risk

Investment is on expectation of return. Investment costs, but if there is a return that exceeds cost after a certain period of time the investment has significance. Let's consider a simple example here. Invest I at the time of t = 0 and return R at the time of t = 1 . Simply put, I & lsaquo; R profits from investment. However, R can not be obtained from the investment until after a certain period of time. Supposing to borrow investment funds (interest rate is r ), if you get a return and you are repaying the principal and interest, the cost is I (1 + r) , And R - I (1 + r) is a return on investment. In this way not only the amount of the return, but also that time will influence investment decision. The discounted present value is a value obtained by converting the economic value of different points on the time axis into the value at a certain point so that it can be compared by absolute amount. In this example, R / (1 + r) represents the value in the return t = 0 . If R / (1 + r) - I is positive, investment will benefit from investment.

Next, let's consider a case where you get a fixed amount of return R every term if you make one investment. In this case, the present value R / (1 + r) , t = 2 of R in the t = 1 < Current value of R in the period R / (1 + r) ² , t = 3 and the present value of R , such as R / (1 + r) ³ . If the fixed amount of return for each term is up to three, it will be the total of the present value of each of the three terms. If R lasts forever, it is the sum of infinite series and the sum is R / r . The higher the interest rate, the lower the present value. In addition to the case where a fixed amount of return is obtained every year, consider the case where the return increases at every rate growth rate R . The series of returns are R, R (1 + g), R (1 + g) ^{2 , R (1 + g) 3} And so on. From the formula of sum of infinite series, it becomes R / (r - g) . r & lsaquo; g It does not converge unless it is the case. In this way, if you calculate the present value of the future return and compare it with the investment amount, you can evaluate the investment case.

There are mainly three ways of evaluation. (1) Of the several investment projects, choose the one with the highest net return (present value of future return - investment amount). (2) If the return goes over a certain period of time, choose the project that can recover the investment amount as quickly as possible. (3) Include the discount rate (interest rate) as unknown number r and find the future value of return = r when the investment amount holds. The meaning of this r represents the maximum discount rate (interest rate) at which net return can be secured, and as this value increases, the uncertainty of the future interest rate can be dealt with. Let's consider the case where there is uncertainty next. At the time of t = 0 , make investment I and return at probability p at t = 1 It is assumed that there is var> R . Probability 1 - p with return 0 . Since the net present value is R / (1 + r) - I with the probability p , the expected value is p (R / r) - I) + (1 - p) (0 - I) = p (R / (1 + r)) - I The smaller the p , the lower the investment expectation.

Generally, if there is uncertainty in return, multiplying the net present value when a return is obtained p will be the expected value of the net present value. It is possible to compare investment projects with magnitude of expected value. As mentioned above, in the case of uncertainty, standard deviation (risk) as well as expectation value must be taken into account. Even for projects with high expected values, if the risks are large, in the case of risk-averse investors, they are avoided. For each investment item, plot the investment items with standard deviation (risk) on the horizontal axis and expected value on the vertical axis. If the expected values ​​are the same, the smaller standard deviation is preferred. If the standard deviations are the same, the one with the larger expected value is preferred. That is, in the figure, the item in the upper left direction is preferred.

Interest and investment (in the absence of uncertainty)

Let's assume that there are five investment projects, A, B, C, D and E. I show the case without uncertainty. Five projects are on the vertical axis of the figure. From the relationship with the equal utility line, A, B, C, D, E are preferentially preferred. Assuming that the investment budget is 10 million yen, A and B will be executed within the budget frame. Investment projects can be executed beyond the budget if borrowing funds from financial institutions. Let's consider financing every investment project that exceeds the budget. The interest rate is r %. If the return on investment is the rate of return, which is greater than r %, you can make a positive profit even if you pay the interest cost. In other words, it will be executed from projects with high return on investment among investment projects, and the procurement method will start from the cheapest procurement method, for example, own funds (interest rate 0%) and choose a procurement method with high interest rates. By adding investment projects, the rate of return decreases steadily and the interest rate rises. Execute in order of A, B, C, and if it is D for the first time, it will be executed only up to A, B, C if [return rate << var> r %]. It is implemented if the interest rate r % goes down and becomes [rate of return> r %]. In other words, if the interest rate goes down, more investment will be made, and if the interest rate rises the investment will be less.

Interest rate and investment (when there is uncertainty)

Let's assume that there are five investment projects, A, B, C, D and E. This time shows the case where there is uncertainty in the case. Five projects are on the plane of the figure. From the relationship with the equal utility line, C, D, E, A, B are preferentially preferred. If investment budget is 10 million yen, C and D can be executed within the range of the budget. Unlike when there is no uncertainty, even if the rate of return is positive, the resulting return is not always positive. Risk is evasive, so if the standard deviation (risk) is large, the utility value will be low, sometimes you give up. If there is no uncertainty, arrange the items in descending order of the profit rate and execute as long as they exceed the interest rate. If there is uncertainty, we arrange matters in descending order of utility value, but since this is not an amount unit, we can not compare magnitude with magnitude. Let's say you draw a line somewhere, say, C, D, E, for example. If the interest rate declines here, the procurement cost will decrease, so the risk (standard deviation) will not change, but the expected value will rise in any case, so the utility value of all the projects will rise. Therefore, if it is decided to execute more than a certain utility value, for example, C, D, E, A will be implemented. As long as the risk (standard deviation) does not change, investment will increase due to declining interest rates. However, as the risk (standard deviation) rises, the utility value falls in every case. Then, if it is decided to execute more than a certain utility value, for example, only C and D will be executed. If the risk (standard deviation) rises, investment will decrease even if the interest rate does not change.

Interest rate policy and investment

In the absence of uncertainty, investment will be suppressed if interest rates rise, and investment will be promoted if interest rates decline. The central bank's interest rate policy is based on this idea. If the economic recession occurs, it will lower the interest rate, encourage companies to invest, restore the economy through purchase of investment and increase production. If the economy overheats, restrain investment by raising interest rates and suppress overheating. However, if there is uncertainty, this is not the case. When the economy is good, it becomes risk preferential, and if the economy goes bad it becomes risk averse. When the recession occurs, the risk is conscious and the utility value of the investment case falls. Even if the central bank lowers the interest rate to promote investment, if the utility value of the investment case is greatly reduced, the investment will not be executed and the interest rate policy will not work.

Loans and risks

In the case of financial institutions conducting loans, if the risk increases without changing the expected value, the utility value of the loan project will decline and the number of loans will be increased. Even if the risk rises but the expected value also rises, the utility value of the loan project does not decrease and the loan case is sometimes implemented. Risk is subjective and it is difficult to measure the degree of risk. Meanwhile, the expected value can be measured at the interest rate level if it is a loan project. Simply set the repayment rate as p , then ((1 + r) I - I) p + (- I) (1 - p) is the expected value . When the risk increases and the repayment rate p decreases, the expected value also decreases. As the risk increases, the utility value decreases greatly if the expected value drops. In order to establish a loan, it is necessary to raise the interest rate r to compensate for the decrease in the utility value due to the increased risk. Interest rates change according to risk. Risks can not be observed, but interest rates can be calculated, so the degree of risk can be inferred by changes in interest rates. Risk premium refers to the increase in interest rates on the reference interest rates (for example, government bonds) that are considered to have no risk. The risk premium is an indicator of the degree of risk. Even if the reference interest rate (policy rate or government bond interest rate) is lowered by monetary policy, individual interest rates do not decrease and remain high as risk becomes conscious because the interest rate is decided by the degree of risk.