Eco 300 Intermediate Micro

Transcription

1 Eco 300 Intermediate Micro Instructor: Amalia Jerison Office Hours: T 12:00-1:00, Th 12:00-1:00, and by appointment BA 127A, aj4575@albany.edu A. Jerison (BA 127A) Eco 300 Spring / 32

2 Applications of indifference curves and budget sets: labor supply and choice under uncertainty. Factor inputs: basic inputs in production: e.g. labor, land, capital, intermediate goods. The market supply curve for any factor input usually slopes upward. For a good produced by a competitive (profit-maximizing) firm, we showed (see Lecture 1) that the supply curve is never downward-sloping. Labor is different from other inputs because individuals, not firms, make the supply decision. A. Jerison (BA 127A) Eco 300 Spring / 32

3 Firms don t have an income effect when not constrained by credit - this means that if they were given more money, it wouldn t change their input and output choice. If they maximize profits without the extra money, the same choice of inputs and outputs maximizes profits with the extra money. Note: In real life, firms are constrained by credit. So they have an income effect. But it is rarely large enough to counteract the substitution effect. Consumers have an income effect. Use income and substitution effect analysis to find the shape of a consumer s labor supply curve. The labor supply curve may bend backwards. A. Jerison (BA 127A) Eco 300 Spring / 32

4 24 hours of day are divided into hours of work and hours of leisure. Leisure includes all non-work activities (including unpaid work done inside the home). Assume leisure is enjoyable (gives positive utility) to worker, work is not (gives no intrinsic utility). but work generates income, which is enjoyable (gives positive utility) A. Jerison (BA 127A) Eco 300 Spring / 32

5 Income/ Expenditures ($ per day) 24w Slope = -w 24 Leisure (hours pe Day) A. Jerison (BA 127A) Eco 300 Spring / 32

6 A worker chooses how many hours a day to work. The wage rate equals the amount of money paid to worker for 1 hour of work done. The wage rate measures how much worker values leisure. The hourly wage is the amount of money a worker gives up in order to enjoy 1 hour leisure (we assume that workers can choose how many hours a day they work). Therefore the hourly wage is price of 1 hour leisure A. Jerison (BA 127A) Eco 300 Spring / 32

7 When the wage rises, the price of leisure rises. A change in choice of leisure due to a wage change has two components: A substitution effect and an income effect. Substitution effect: higher price of leisure causes workers to substitute work (money) for leisure. Income effect: higher wage gives workers more money to spend on many goods, among them leisure. If a higher wage causes worker to work more hours, it is because substitution effect led the worker to substitute work for leisure - the substitution effect has dominated. If a higher wage caused worker to work fewer hours, it is because the income effect allowed the worker to buy more leisure - the income effect has dominated. A. Jerison (BA 127A) Eco 300 Spring / 32

8 Income/ Expenditures ($ per day) Possible choices leading to a backwards-bend Labor supply curve 24 Leisure (hours pe Day) A. Jerison (BA 127A) Eco 300 Spring / 32

9 If income effect dominates substitution effect, a higher wage leads worker to work fewer hours. If substitution effect dominates income effect, a higher wage leads worker to work fewer hours. A. Jerison (BA 127A) Eco 300 Spring / 32

10 Backward-bending labor supply curve Such a curve arises if: At high wages the income effect dominates the substitution effect. At low wages the substitution effect dominates the income effect. A. Jerison (BA 127A) Eco 300 Spring / 32

11 Wage ($ per Hour) Quantity of l (hours per d A. Jerison (BA 127A) Eco 300 Spring / 32

12 Women s and men s labor supply Why has the labor supply of women increased since the 1950 s and the labor supply of men decreased? Consider a couple, male and female. Suppose the man works more hours at a higher wage rate than woman. The man is then called primary worker, woman secondary worker. A. Jerison (BA 127A) Eco 300 Spring / 32

13 Assume they split their incomes evenly. Call unearned income the portion of each person s income that comes from the other s earnings. Draw their budget sets: The secondary worker has a high unearned income and a low magnitude of slope of the budget line, the primary worker has a low unearned income and a high magnitude of slope of the budget line. Assume they have identical preferences. A. Jerison (BA 127A) Eco 300 Spring / 32

14 Now suppose the wage of primary worker increases by 20% and wage of secondary worker increases by 25%. Both unearned incomes increase, but the primary worker s unearned income increases by more than the secondary worker s. Both slopes increase, but the secondary worker s slope increases by more than the primary worker s. Draw the new maximizing indifference curves. It is possible that with the same indifference curves, the man works less and the woman works more. A. Jerison (BA 127A) Eco 300 Spring / 32

15 Income Men Income Women Leisure A. Jerison (BA 127A) Eco 300 Spring / 32

16 This idea may partly explain why men s labor supply has decreased and women s has increased since the 1950 s. A. Jerison (BA 127A) Eco 300 Spring / 32

17 Choice under Uncertainty Examples: Insurance demand, Financial portfolio choice Represent demand for insurance by reinterpreting the consumer model (not model in ch. 5) Suppose there is a possibility of a loss occurring. Let y = the individual s net income if the loss does not occur Letx = the individual s net income if the loss occurs A. Jerison (BA 127A) Eco 300 Spring / 32

18 π x = probability of loss π y = probability of no loss π x + π y = 1 (either the loss occurs or it doesn t) A. Jerison (BA 127A) Eco 300 Spring / 32

19 The market basket (x, y) shows the individual s income in both cases (loss and no loss). Expected income = π x x + π y y. A fair line shows all points with the same expected income π x x + π y y = C for some constant C. Slope = π x /π y Note that this line has the same form as a budget line where the π x and π y are the prices and C is the expected income. Now the interpretation will be different however. A. Jerison (BA 127A) Eco 300 Spring / 32

20 Income when No loss occurs A fair line Income when Loss occurs A. Jerison (BA 127A) Eco 300 Spring / 32

21 The fair line represents all the combinations of income in the two different states that have the same expected value. The probability of the loss occurring is fixed along the line. 45% certainty line (complete insurance): Along the 45% certainty line, net income is same whether or not loss occurs - there is no risk at points on the 45% line. By buying insurance, the consumer reduces his income if there is no loss (y), but increases his income if there is a loss (x). Thus he moves closer to the 45% line by buying insurance. A. Jerison (BA 127A) Eco 300 Spring / 32

22 Preferences A risk neutral consumer cares only about expected income. Such a consumer s indifference curves are fair lines. In other words, the indifference curves are lines with slope π x /π y. If π x and π y change, the indifference curves change slope so that the slope of the indifference curves again equals π x /π y. A. Jerison (BA 127A) Eco 300 Spring / 32

23 Suppose the loss probability is tiny. The slope of an indifference curve tells you how much income in the no-loss state the consumer would give up for an additional dollar in the loss state. With a tiny loss probability, he would be willing to give up very little income in the no-loss state in exchange for an additional dollar in the loss state. So the slope of the indifference curve is almost zero in this case. A. Jerison (BA 127A) Eco 300 Spring / 32

24 On the other hand, if the loss is almost sure to happen, he will give up a lot of income in the no-loss state in exchange for a dollar when there is a loss. So the slope of the indifference curve is very steep in this case. A. Jerison (BA 127A) Eco 300 Spring / 32

25 A risk-averse consumer is willing to give up some expected income in exchange for less riskiness. A risk-averse consumer s indifference curves look standard, except possibly with kinks. For a risk-averse consumer, the highest indifference curve touching a fair line touches it at the certainty point (since the best point on the fair line is the point of certainty) A. Jerison (BA 127A) Eco 300 Spring / 32

26 The endowment is the initial market basket without trade. In the insurance model, trade means buying insurance. Insurance policy: Consumer pays premium p per $1 coverage no matter what (p < 1). The $1 coverage reduces income by p if no loss occurs, raises income by 1 p if the loss occurs. The budget line slope is p/(1 p). Coverage is what they pay you in case of loss. Premium is what you pay them no matter what. A. Jerison (BA 127A) Eco 300 Spring / 32

27 Actuarially fair insurance is defined as a policy giving the insurer 0 expected income. The insurer s expected income from $1 coverage is p π x. (They get p for sure, and lose $1 if the loss occurs). An actuarially fair premium is p = π x, the loss prob- ability. With this premium, the insurer s expected income is pπ y + (p 1)π x. When p = π x, this reduces to 0 (since π y = 1 π x ). With actuarially fair insurance the budget line is the fair line: slope = p/(1 p) = π x /(1 π x ) = π x /π y. A. Jerison (BA 127A) Eco 300 Spring / 32

28 Most insurance is actuarially unfair: premium = p > π x = prob. of loss. The budget line is steeper than the fair line. This is because insurers have costs that they need to cover. Also, they try to make profits. A. Jerison (BA 127A) Eco 300 Spring / 32

29 Conclusions: 1. Actuarially fair insurance: premium = probability of accident. 2. With actuarially fair insurance, a risk averse consumer takes full coverage (on certainty line). 3. With actuarially unfair insurance, a risk neutral consumer takes no insurance. A risk averse consumer takes less than full coverage. 4. With premium lower than actuarially fair, a risk averse consumer takes more than full coverage (meaning that they will end up with more income in the loss state than in the no loss state). A. Jerison (BA 127A) Eco 300 Spring / 32

30 Insurers often don t offer full coverage (customer must pay a deductible if the loss occurs). Insurers also try to prevent customers from getting extra coverage from another insurer. In our model, risk averse consumers never want the extra coverage, so the model does not explain the insurers behavior. One possible explanation is moral hazard: customers might raise the probability of the loss if they gain from it because of insurance. A. Jerison (BA 127A) Eco 300 Spring / 32

31 The same model can be used to explain portfolio choice A consumer invests wealth in asset A, gets return x in state X, y in state Y. The asset is represented by market basket A = (x, y). Expected return of A is π x x + π y y. Consumer can buy A or buy an indexed bond B with sure return b, market basket B = (b, b) on the certainty line. A risk averse consumer prefers A to B only if A is on a higher fair line (A s expected return > b) and maybe not even then. A. Jerison (BA 127A) Eco 300 Spring / 32

32 Diversification: Consumer can spend part of wealth on A, part on B, get return corresponding to any point on segment AB. If only risky A and sure B are available and A has a higher expected return, then a risk averse consumer will put some wealth in A. (A risk averse consumer accepts some risk when compensated by a higher expected return.) A risk averse consumer might want to put some wealth in a third asset C even if its expected return is below b. C must provide insurance against A s riskiness. Market baskets A and C must be on opposite sides of the certainty line, so C gives a higher return when A s return is lower. A. Jerison (BA 127A) Eco 300 Spring / 32