# Problems for Section 161

3. Each of the 6 gallons cost 30 cents in waiting time plus 50 cents in cash. In other words, a rise in price from 50 to 80 cents a gallon sufficed to reduce the quantity demanded by 25 percent (if it had not sufficed the queues would have lengthened until it did). Evidently the elasticity was not zero. Depending on which of the two points along the demand curve is taken as the base in the arithmetic, then, the elasticity is (25/100)/(30/50) = 0.42 or (25/75)/(30/80) = 0.88, for an average of (0.42 + 0.88)/2 = 0.65. More elegantly, consider a constant elasticity demand curve:

Inserting the two observed pairs of Q and P (let Q0 = 100) and dividing one equation by the other yields:

from which, taking logarithms and solving for e, one finds that e = 0.61. An elasticity of 0.61 or 0.65 is not the same as an elasticity of zero. Don't believe everything you read in the newspapers.

5. True. The excess willingness-to-pay created by the low price must somehow be choked off. One way to choke it off is to let people stand in sweltering lines for 6 hours. By contrast, if the museum gives them queue tickets the last person to join the line will not experience as much pain and suffering as he would without the queue tickets. In consequence, more people will join the line, until the last person to join is just barely satisfied with the deal. The result is that the total inconvenience will be the same as before. Instead of standing in line the people will be able to tour the city, but the touring must itself be tiring and boring enough to exactly equal in inconvenience the time saved from standing in line. To put it another way, the number of slots passing by the exhibit cases is a scarcity that must somehow be allocated. The full price (money plus inconvenience) must rise to equal the marginal willingness-to-pay at that quantity.

6. Since there was no evidence of excess demand, the government regulations were apparently not holding down the price. Therefore the removal of the regulations would have no effect. It is possible, indeed, that the regulations merely caused a misallocation of the oil supply, raising rather than lowering prices. There may well be some line of reasoning that favors the more conventional assumption, but it is not simply a matter of the government sitting on oil prices.

8. a. True. The price of coupons will be equal to the difference between the money price and the marginal valuation consumers put on gasoline when its supply is 100 gallons, for coupons bestow the right to buy a gallon, and are therefore worth what the marginal consumer will give for them. Queues will not develop, because the money price plus the value of the coupon will discourage demand to exactly the amount 100 gallons: nothing is gained by standing in line; time wasted in lines is not necessary to ration the gasoline.

b. True. Suppose the government issues coupons for only 50 gallons. Then only 50 can be sold, for a coupon is necessary to buy a gallon. Suppliers will find that they can't sell the 50 additional gallons they would be willing to offer at the controlled price. So they offer less. So the supply price necessary to get them to supply the smaller amount falls. Meanwhile, with a smaller amount purchasable, consumers value the marginal gallon more. The marginal valuation increases, that is, consumers move up their demand curves. To maintain the equality,

^"monej Pcoupon ^marginal valuation the price of coupons must rise to the difference between the supply price (at the lower, 50-gallon supply) and the marginal valuation.

c. True. Issuing enormous numbers of coupons drives their price to zero. That is, they are not a constant constraint on gasoline purchases. In consequence, they no longer ration the available quantity, and time must do it. Answer the following question: what happens when the issue of coupons is only a little above the current amount? Coupons are evidently not literally valueless in this case; but they do not make it certain that one gets a gallon, for there are more coupons than gallons.