1. Suppose a Canadian lumber company has a world monopoly on lumber, so that all lumber purchased by U.S. citizens is bought from this one Canadian lumber company.
(a) Draw a supply-demand graph with linear demand curve and a flat marginal cost curve. Shade in total US surplus on the graph.
(b) Now suppose the U.S. government uses a small tariff. Draw a new supply-demand graph and once again shade in total US surplus.
(c) Now suppose the U.S. government gives the foreign monopolist a small subsidy. Draw a new supply-demand graph and once again shade in total US surplus, making it clear which areas negatively contribute to surplus.
(d) Show, using a new graph, that a price ceiling is the optimal US government policy. However, why might this policy not increase total US surplus as much, or at all, in the long run?
Give an example of something Canada might do in response.
2. Take the scenario from 1(a) and suppose demand is Q(p) = 1000p-3.
(a) Show that p =32m where p is price and m is marginal cost.
(b) From (a) we know that lowering m by 2 cents would cause p to fall by 3 cents. Suppose marginal cost is first m1 = $2, but then the U.S. government subsidizes the Canadian lumber company by 2 cents per unit so that the new effective marginal cost is m2 = $1.98. Show that this subsidy actually increases US total surplus. (Hint: the picture below may help.)
3. Suppose there is a perfectly competitive corn industry in the US with a constant marginal cost of $6 per bushel of corn. There are no foreign producers of corn. Canadian demand for US corn is Q = 200p4 .
(a) How would the US government maximize US total surplus using an export tariff? Who receives this gain in surplus, relative to free trade?
(b) How would the US government maximize US total surplus using an export quota? (You can provide an expression for the quota quantity; no need to calcualte it.) Now who receives the gain in surplus, relative to free trade?
4. Suppose a domestic monopolist competes with imports from foreign firms. The government sets a quota rule that foreign sales, Qf , can be no more than a fixed percentage, α, of Qd. That is, Qf = αQd and total quantity is Q = Qd(1 + α). So the monopolist's profit is π = [p (Qf + Qd) - m] Qd= [p (Qd (1 + α)) - m] Qd= [p (Q) - m] Qd
Show that this quota does not restrain market power: the price is the same under monopoly as under trade with this import quota. (Hint: show that we have the same Lerner Index Rule. To do this, find the FOC for the monopolist, carefully applying the chain rule. There are some footnotes in the textbook's "Creation of Domestic Monopoly" subsection, under the "Creating and Battling Monopolies" section, that may help!).