Problem 1: Assume the salmon-packaging industry comprises a price leader and two small firms that behave competitively. The cost functions of the three are:
price-leader........................CL = 0.05qL2 + 1.75qL
competitive firms............. C1 = 0.05q12 + 3q1
C2 = 0.1q22 + 3q2
The market demand is q = 50 - 5p
(a) Determine the short-run supply curve for the competitive firms.
(b) Determine the residual demand curve facing the price leader.
(c) Calculate the profit-maximizing output for the price leader.
(d) What is the market price given the price leader's output in (c).
(e) How much does each competitive firm produce?
Problem 2: Suppose that the demand for crude oil is given by:
Q = -2000P + 70,000
where Q is the quantity of oil in thousand of barrels per year and P is the dollar price per barrel. Suppose also that there are 1000 identical small producers of crude oil, each with marginal costs given by:
MC = q + 5
where q is the output of the typical firm.
(a) Assuming that each small producer acts as a price taker, calculate the market supply curve and the market equilibrium price and quantity.
(b) Suppose a practically infinite supply of crude oil is discovered in New Jersey by a would-be price leader and that this oil can be produced at a constant average and marginal cost of $15 per barrel. Assuming that the supply behavior of the competitive fringe described in part (a) is not changed by the discovery, how much should the price leader produce in order to maximize profits? What price and quantity will now prevail in the market?
(c) Sketch the demand curve. Does consumer surplus increase as a result of the New Jersey oil discovery? How does consumer surplus after the discovery compare to what would exist if the new Jersey oil were supplied competitively?
Problem 3: The Potash Corporation of Saskatchewan (PCS) and two small producers supply a particular fertilizer market. The small producers behave as competitive price takers; PCS as a price leader. The marginal cost curves of the small producers are, respectively:
MC1 = 3 + 0.1q1
MC2 = 3 + 0.2q2
The marginal cost of PCS is:
MCS = 2 + 0.04qS
The market demand for fertilizer is:
Q = 80 - 10p.
(a) What is the aggregate supply curve for the small producers?
(b) What is the residual demand curve facing PCS?
(c) What is the profit maximizing level of PCS production?
(d) What price will PCS establish?
(e) What will be the quantity supplied by each of the two small producers?