Quotas - Quantitative Problems

1. In the U.S., daily supply and demand for a particular good are given by the equations:

Q^S = -5 + 10P_U.S.

Q^D = 130 - 5P _U.S.

where

Q^S = quantity supplied (millions of units per month).

Q^D = quantity demanded (millions of units per month).

Assume the U.S. is a small country in the market for this good. Further, assume that in the rest of the world, the market price for this good (P_ROW) is $5.

a. Before trade opens up, what are the values of the equilibrium price and quantity in the U.S.?

b. If trade opens up, what will be the quantity of U.S. imports per month?

c. Suppose the U.S. imposes a quota of 45 million units per month on this good. What will be the price U.S. consumers will pay for the good now?

d. Suppose that the U.S. provides import licenses to U.S.-owned import companies without charge, based on some fixed formula (e.g. past market share, or a lottery). This means that U.S. import companies are unable to influence how many licenses they are issued. Calculate welfare change caused by the quota for each of the following groups. (Answers should be in dollars)

(1) U.S. producers

(2) U.S. consumers

(3) U.S. import companies

(4) The U.S. as a whole

2. Now, assume that the U.S. is a large country in this market, with the same supply and demand equations given in question 1. above. Further, assume that supply and demand equations in the rest of the world are given by the following equations:

Q^S_ROW = 20 P_ROW

Q^D_ROW = 90 - 10 P_ROW

1. Before trades opens up with the U.S., what are the values of the equilibrium price and quantity in the rest of the world?
2. If trade opens up with the U.S., and there is no tariff or quota, what will be the world price of this good?
3. Suppose, after trade opens up, the U.S. imposes a quota of 45 million units per month on this good. What will be the price U.S. consumers will pay for the good now? What will be the price the rest of the world's consumers pay for the good?

3. For the large country case you've just explored, consider the following four different license-allocation methods for enforcing the quota:

(a) The U.S. government auctions off licenses to the highest bidder among U.S.-owned import companies.

(b) The U.S. government offers licenses to U.S. import companies based on the "legal case" they make for receiving them. [This is an example of a "resource using" license allocation mechanism.]

(c) The U.S. government allows the ROW governments to distribute export licenses within their own countries as they see fit. The ROW governments decide to give the licenses to their own producers without charge, based on a "fixed formula" (e.g., based on their share of the total market in recent years).

For each of these allocation mechanisms, determine the monthly welfare changes (in dollars) for each group in the table below (or on the next page). Use a "+" sign for gains, and a "-" sign for losses, and give numbers (millions of dollars per month)