1. Consider two firms out of a competitive industry. They have the following technologies: C1(Y) = y2 + 2y; C2(y) = 1.5y2 + 3y. Show these firms' individual supply functions on a clearly-labelled graph. Construct an aggregate supply function for these two firms on your graph.
2. Consider three firms out of a competitive industry. They have the following technologies: C1 = y2 +9; C2 = y2 + y + 9; C3 = y2 + 2y+ 9.
a. For each firm derive the SAC, SMC and AVC. Show these curves on three graphs, one for each firm.
b. Suppose that in the short run the market price is 7. Show each firm's profit on your graphs. Should all of these firms produce? Explain.
3. A monopolist has access to an industry with market demand
P = 10 - y
where y is the firm's quantity. Its cost function is
C(y) = 2y
a. Determine the firm's profit maximizing quantity. Show your outcome on a graph. What is the firm's profit? Compute the point-elasticity of demand at the profit-maximizing output.
b. Now suppose the firm's cost function is C(y) = 4y
Again determine the profit-maximizing quantity, profit and the elasticity at the profit-maximizing quantity. (No graph is required in this case.)
c. Essentially, we have two types of monopolist. Which monopolist type operates at the higher level of elasticity? Why?
d. Prove that for any linear demand, p = a - by, and constant marginal cost, c, that a monopolist would never ever operate at a point elasticity less than 1.