Assume that demand for rollerblades is given by D(p) = A ? p. The cost function for all the firms is C(y) = wy2 + f , where f is a fixed set-up cost. The marginal cost of production is MC(y) = 2wy. Suppose that the industry is perfectly competitive.
1. Identify a competitive firm's supply function. If there are n firms in the industry, determine the industry supply?
2. Find expressions for the competitive equilibrium price and the quantity if there are n firms in the industry. Determine the equation for how much each firm produces? Calculate the equation for the profit of each firm?
3. Assume w = $4, A = 100, f = $100, and n = 2. Using the equations you derived in part (2), what is the equilibrium price and quantity? Firm profits and supply? Using two diagrams, graph this competitive equilibrium. In one diagram demonstrate the market equilibrium. In the second, demonstrate equilibrium position of a representative firm. On this second diagram make sure you indicate profit-maximizing output of a firm as well as the profit earned.
4. Is the equilibrium you found in part (3) a short-run or long-run equilibrium? Why? If the industry is not in long-run equilibrium, discuss the adjustment process that will occur.
5. For the parameter values given in part (3), identify the long-run competitive equilibrium. On the two diagrams from part (3), indicate the long-run equilibrium. Calculate the long-run equilibrium number of firms?