Problem 7: Extension of Monopoly. A monopolist sells shoe making machines to a perfectly competitive market of shoe manufacturers. The marginal cost of producing a shoe machine is 1. A shoe manufacturer can use combinations of machines and labor to produce shoes. If a shoe manufacturer uses K machines and L units of capital, it can produce Q = L K shoes. Price of labor is Pt = 1. (a) Draw a diagram of the industry, with an arrow from any seller to any buyer. Specify the upstream and downstream firms. 3 (b) Assume that a shoe manufacturer plans to produce 64 shoes. Draw the isoquant curve and identify at least three points on it. (c) Assume that the price of shoe machines is Pk = 4. To produce 64 shoes, what combination of capital and labor should a shoe firm use? (d) Now assume that the shoe machine firm merges with one of the shoe firms (and can therefore acquire shoe machines at marginal cost). To produce 64 shoes, what combi- nation of capital and labor should the merged firm use? Hint: You can use the formula MPK MPL *. In this problem, M PK = L and MPL = K. %3D PL