Annual demand for rock climbing shoes is Qd = 50,000,000 P-2 a. (1) Prove that the formula above implies a constant elasticity of demand of εp = -2. b. (5) Suppose the industry is competitive, and each firm's total cost of production is TCi = 100 qi. What type of market supply function does this give rise to? Find the market price and quantity. If there are 4 identical firms supplying this market, how many pairs of shoes does each firm sell annually, and what is each firm’s annual profit or loss? c. (3) Now suppose the market for these shoes is supplied by a single monopolistic firm, having the same cost function as in part b. Find the new market quantity, price and the monopolist’s profit or loss. (Note in this particular case, marginal and average costs to produce the good are not affected by the number of plants, since we have no fixed costs and a constant marginal cost)