Suppose the market for tennis shoes has one dominant firm and five fringe firms. The market demand is Q=400-2P. The dominant firm has a constant marginal cost of 20. The fringe firms each have a marginal cost of MC=20+5q.a.Verify that the total supply curve for the five fringe firms is.b.Find the dominant firms demand curve.c.Find the profit-maximizing quantity produced and price charged by the dominant firm, and the quantity produced and price charged by each of the fringe firms.d.Suppose there are ten fringe firms instead of five. How does this change your results?e.Suppose there continue to be five fringe firms but they each manage to reduce their marginal cost to MC=20+2q. How does this change your results?

a. The total supply curve for the five firms is found by horizontally summing the five marginal cost curves, or in other words, adding up the quantity supplied by each firm for any given price. Rewrite the marginal cost curve as follows: Since each firm is identical, the supply curve is five times the supply of one firm for any given price: b. The dominant firms demand curve is given by the difference between the market demand and the fringe total supply curve: c. The dominant firm will set marginal revenue equal to marginal cost. The marginal revenue curve can be found by recalling that the marginal revenue curve has twice the slope of the linear demand curve, which is shown below: We can now set marginal revenue equal to marginal cost in order to find the quantity produced by the dominant firm, and the price charged by the dominant firm: Each fringe firm will charge the same price as the dominant firm and the total output produced by the fringe will be Each fringe firm will produce 12 units. ??Qf?P?20?60. d. We need to find the fringe supply curve, the dominant firm demand curve, and the dominant firm marginal revenue curve as was done above. The new total fringe supply curve is Qf = 2P-40. The new dominant firm demand curve is QD = 440 – 4P. The new dominant firm marginal revenue curve is The dominant firm will produce where marginal revenue is equal to marginal cost which…

occurs at 180 units. Substituting a quantity of 180 into the demand curve faced by the dominant firm results in a price of $65. Substituting the price of $65 into the total fringe supply curve results in a total fringe quantity supplied of 90, so that each fringe firm will produce 9 units. The market share of the dominant firm drops from 75% to 67%. e. Again, we will follow the same method as we did in earlier parts of this problem. Rewrite the fringe marginal cost curve to get The new total fringe supply curve is five times the individual fringe supply curve, which is just the marginal cost curve: The new dominant firm demand curve is found by subtracting the fringe supply curve from the market demand curve to get The new dominant firm marginal revenue curve is The dominant firm will produce 180 units, price will be $60, and each fringe firm will produce 20 units. The market share of the dominant firm drops from 75% to 64%.