Uncertainty and information

With reference to federal legislation assuring to every resident in the U.S.A. medical care by the physician and hospital of his choice, free and with no special taxation: Appraise the proposal as to effects upon general welfare, assuming that the alternative is the sale of medical insurance, not subsidized, but with the same distribution of personal income effected by cash “relief”.

Many families carry life insurance for the husband, and very few carry it for the wife or children. There have been several attempts to explain this. Some say that the loss from the death of the wife or children is mostly a psychic loss, and psych losses cannot be insured. Others say that the loss from the death of the wife or children is too small to be worth insuring. Evaluate these arguments. Can you give an explanation consistent with rational behavior?

The margin in stock trading is the fraction of the price of the stock which the trader must supply and the balance is lent to the trader by the broker. Hence the margin represents the trader’s equity and is analogous to a down payment. Assume there is no government regulation of the margin and that brokers are free to set any margin they please and to charge any interest rate they please on the loan they extend to traders. Assume there is perfect competition in the brokerage industry.

Would you expect margins to be higher during periods of “active” speculation?

Would you expect higher margins when stock prices are rising then when they are falling?

Would a rise in the interest compensate for or be equivalent to a rise in the margin?

II. Fill in the blanks in the following questions.

Consider three demand curves for commodity X: A for given money income and other prices; B, for given apparent real income in Slutsky’s sense; C, for given real income in Hick’s sense. Let all three curves go through the point $(p_o,x_o)$

If X is a superior good, then for a price lower than $p_0$, the quantity demanded will be larger for_____ than for _____. (Insert A, B, C, in correct spaces.)

If X is an inferior good, then for a price lower than $p_0$, the quantity demanded will be larger for _____ than for _____.

Suppose p_0 = \5$,$X_0 = \$20$, the corresponding money income \1,000$,andtheincomeelasticityofdemandforXis2.Supposethatataprice$\$4$, the quantity demanded on curve A is 25. Then the income compensation required to pass from A to B is \$_____ (be sure to indicate sign of change) and the quantity demanded on curve B is _____.

Blank is indifferent whether he wagers \1$ateven-moneythatacoinheregardsasfairwillcomeupheads.Heiseagertowager$\$1$ against \3$(i.e.,hepays$\$1$ if he loses, receives \3$ifhewins)thatheadswillcomeuptwiceintwosuccessivethrowsofthiscoin.(Heregardsthethrowsasindependentandsothechancesoftwosuccessiveheadsasoneinfour.)Lettheutilityofhisincomeifheloses$\$1$ be 100; if he wins \1, 101. Then the utility to him of his present income can be taken to be _____ (insert a number); the utility to his present income plus \$3$ _____ (insert the most accurate statement the evidence permits).

I. Indicate which alternatives, if any, are correct or fill in the indicated blanks. Where you think it required, briefly justify your answer.

Marginal revenue (a) cannot (b) may (c) must rise as output increases.

A monopolized product initially sells for $1. A tax is imposed on the product. A tax of t cents per unit will reduce marginal revenue at the pre-tax output (a) more, (b) less, (c) the same amount, (d) sometimes more sometimes less than a tax of t per cent.

In the preceding example, the imposition of a tax of t cents will lead the monopolist to reduce output (a) more, (b) less, (c) the same amount, (d) sometimes more sometimes less than a tax of t per cent.

A reduction in demand for a product is followed by a rise in quantity sold despite no change in conditions of supply. It follows that the product is being produced (a) in a competitive industry with increasing returns, (b) in a competitive industry with external diseconomies, (c) by a monopolist, (d) this result is impossible under any of the preceding conditions.

Assume that the government has been supporting the price of wheat by buying any wheat offered to it at its support price. Suppose it abandons the program. In the new position of long period equilibrium the total amount received by producers will rise (a) only if the market demand for wheat is inelastic in the range between the support and new price, (b) only if the market demand for wheat is elastic in this range, (c) whatever the demand elasticity, (d) under no circumstances.

An individual buys four commodities, W, X, Y, and Z, currently spending one-quarter of his income on each. The income elasticity of W and X are 2; of Y, 1. The income elasticity of Z is _________?

Consider three demand curves for commodity X: A, for given money income and other prices; B for given apparent real income in Slutsky's sense; C, for given real income in Hicks' sense. Let all three curves go through the point $(p_o,x_o)$. If X is a superior good, then for a price higher than $p_o$, the quantity demanded will be larger for ____ than for ____ than for ____ (Insert A, B, C, in correct spaces).

Suppose p_o = \2$,$x_o = 40$,thecorrespondingmoneyincomeis$200, and the income elasticity of demand for x is unity. Suppose that at a price of $2.50, the quantity demanded on Curve A is 20. Then the income compensation required to pass from A to B is $ _____ (be sure to indicate sign of change) and the quantity demanded on curve B is _____.

If long run average cost (LRAC) equals short run average cost (SRAC) at an output on the falling segment of the LRAC curve then short run marginal cost (SRMC) (a) exceeds, (b) equals, (c) is less than long run marginal cost (LRMC) at that output.

If LRAC is rising and less than SRAC, then SRMC is (a) rising, (b) falling, (c) greater than SRAC, (d) less than SRAC.

In a discussion of the World Series last fall, Jones offered to take either side of a bet with Smith involving a payment of $2 by one party if the Pirates won, of $1 if the Yankees did. It follows that Jones' estimate of the probability that the Yankees would win is _____ and that his utility function of income is (a) concave upward, (b) linear, (c) concave downward, (d) not concave upward, (e) not concave downward.

Alternatively, Jones refuses to take either side of the preceding bet but offered to take either side of a bet involving a payment of $200 by one party if the Pirates won or of $100 if the Yankees did. This behavior (a) contradicts or (b) is consistent with the expected utility hypothesis.

(a) Complaints are often heard about the “high” incomes of bootleggers in dry states, or gamblers where gambling is illegal, or smugglers, etc. Are high incomes in such cases evidence of the success or the failure of the laws? Explain your answer.

(b) A man buys a ticket in a lottery and wins. View this as a business transaction. How much, if any, of his prize is properly regarded as “profit”? Does your answer use the concept of “profit” implicit in the common statement “entrepreneurs seek to maximize profit”? Justify your answer and indicate the difference, if any, between the two concepts.

Discuss the relation between forward (and/or futures) prices and spot prices on commodity markets and foreign exchange markets and the role of “speculators” and “hedgers” in these markets. State some of the leading theories about this relationship and discuss the kinds of evidence used in testing them.

Assume the following simple world, in which you are asked to determine the optimum rate of automobile accidents.

The only type of accident which occurs is that a car may run into a house. The damage is then always $200.

The probability of an accident will be greater,

…the faster automobiles are driven

…the closer houses are set to the highway.

Assume explicitly any additional information you need to define the socially optimum accident rate. What mechanism, if any, could you design to achieve it?

In most states it is illegal for drug stores to advertise the prices of prescription drugs. A customer can find out the price of a prescription drug only by asking the pharmacist in person. In addition only pharmacists licensed by the state are allowed to dispense drugs and every drug store must employ at least one licensed pharmacist. One can become a licensed pharmacist by passing an examination administered by the state and written by a board of pharmacists. Finally, a pharmacist must fill a prescription exactly as it is written by the physician and may not substitute a generically equivalent drug.

What would happen if pharmacists were allowed to advertise the prices of prescription drugs?

What would happen to the price of drugs if pharmacists were allowed to substitute any drug from a specified list in place of the prescribed drug?

Indicate whether each of the following statements is true (T), false (F), or uncertain (U), and state briefly the reason for your answer. It is to be understood that in each question the appropriate “other things” are to be held constant.

1. The imposition of a minimum wage for labor of type X higher than the preceding wage leads to an increase in the number of laborers of type X employed. It follows that labor of type X is hired under monopsonistic conditions.

2. Under both competition and monopoly in the product market, marginal value product of a factor to a firm is equal to marginal physical product of the firm times marginal revenue to the firm from the sale of the product.

3. Marginal productivity analysis shows that, in the absence of monopsony, a laborer gets as a wage his marginal value product. If this analysis is correct, it follows that unions can raise wages in the absence of monopsony only if they either make each worker more efficient, or increase demand for the product, or make the demand for the product more elastic.

4. The law of variable proportions (or diminishing returns) is contradicted by the fact that agricultural output of this country has increased tremendously despite a decrease in the proportion of the working population on farms.

5. The rate of interest is equal to the rate of time preference of consumers.

6. At present levels of operation, three quarters of the total cost of the XYZ railroad is overhead cost that does not vary with traffic, only one quarter is variable cost. It follows that marginal cost is much less than average cost.

7. The demand curve of an individual firm for a factor of production is identical with its marginal value productivity curve for the same factor of production.

8. The demand curve of a firm for a factor of production is a meaningless concept if the firm is a monopsonistic purchaser of that factor.

9. A declining long run supply curve is impossible in a competitive industry.

10. Marginal factor cost is equal to the price per unit of a factor whenever the product market is competitive.

11. According to the theory of joint demand, the absolute value of the elasticity of derived demand for a factor of production will be smaller the more inelastic the supply of that factor.

12. The fact that individuals do not choose occupations solely on the basis of their pecuniary attractiveness helps explain why the supply curve of labor for a particular occupation has an elasticity greater than zero.

13. If all types of services were used only in fixed proportions, a marginal-productivity theory would be neither necessary nor possible.

14. Our society is often described as a “profit” economy or “profit-maximizing” economy. The word “profit” is here used in the same sense as in the uncertainty theory of “profit.”

15. “Profit” as defined in the uncertainty theory of profit is the expected return to any factor assuming uncertainty over and above the guaranteed expected income it can obtain if it assumes no uncertainty.

16. If one income is higher than another before income tax it will also be higher after a progressive income tax, provided only that the marginal tax never exceeds 100%. It follows that if one accepts the theory that individuals act as if they sought to maximize their income, he must also accept the conclusion that such taxes do not alter individual's actions and hence are not shifted.

17 and 18. A minimum wage law is repealed. The wage rate of a class of workers hired under competitive conditions was equal to the minimum before repeal and falls after repeal. It follows that:

17. The total wage bill for this class of labor will rise, remain constant, or fall, according as the elasticity of demand for labor of this class is greater than, equal to, or less than unity in absolute value.

18. The quantity of labor of this class employed will fall, remain constant, or rise according as the elasticity of supply of labor of this class is positive, zero, or negative.

19. The great technological improvements in the past few decades in the production of synthetic fibers (rayon, nylon, etc.) and associated decline in their relative price has, among other effects, tended to raise the price of meat in general, especially of lamb and mutton.

20. At the same time, stringent rationing of meat consumption in Great Britain, by tending to offset this effect, has improved the competitive position of the synthetic fiber industry, and so enabled it to expand more than otherwise.

Suppose the traffic department would like to enforce parking regulations in an efficient way. Assume that each person has the choice of parking illegally or legally; the latter costs X dollars per “day” and the former, if one is caught, causes a fine equal to F dollars per time caught.

Assume first that the sole aim of the traffic department is to discourage illegal parking at minimum cost. Assume also that all drivers simply try to maximize expected money income. How frequently should the traffic department inspect parking in order to achieve its aim?

If all drivers maximized expected utility and had diminishing marginal utility of income, (but there is no utility or disutility from disobeying the law), how would this affect your answer? If they had increasing marginal utility of income?

Suppose the traffic department received all the fines and desired just to maximize its expected income. How would your answer to 1. be affected?

How does your answer to a. and c. depend on F, the size of the fine, and X, the cost of legal parking?

Explain the following accurate statement: The gain from search activity is related to the dispersion of prices charged by different sellers. The gain is also related to the fraction of the individual’s income spent of the good and its income elasticity. Give a real world example of a good whereby the buyer searches a little and another good whereby the buyer searches a lot. Explain why.

Assume that the cost of a unit of search is the same for all goods and all have the same price variability in the absence of search.

(a) Show that if the cost of search is proportional to income, the rich will search more and thus pay less for goods with income elasticities greater than unity and search less and pay more for goods with income elasticities less than unity.

(b) On the basis of these results, do you expect the poor to pay more for good? Are there policy implications in your findings which may increase the welfare of the poor?

Evaluate: “A bird in the hand is worth six in the bush.”