In footnote 7 we showed that for a utility function for two goods to have a strictly diminishing MRS (i. e., to be strictly quasi-concave), the following condition must hold: Uxx U2 y 2 2UxyUxUy 1 UyyU2 x , 0. Use this condition to check the convexity of the indifference curves for each of the utility functions in Problem 3.1. Describe the precise relationship between diminishing marginal utility and quasi-concavity for each case.

Consider the local telephone company, a natural monopoly. the following graph shows the monthly demand curve for phone services and the company’s marginal revenue (mr), marginal cost (mc), and average total cost (atc) curves. 0 2 4 6 8 10 12 14 16 18 20 100 90 80 70 60 50 40 30 20 10 0 price (dollars per subscription) quantity (thousands of subscriptions) d mr mc atc 8, 60 suppose that the government has decided not to regulate this industry, and the firm is free to maximize profits, without constraints. complete the first row of the following table. pricing mechanism short run long-run decision quantity price profit (subscriptions) (dollars per subscription) profit maximization marginal-cost pricing average-cost pricing suppose that the government forces the monopolist to set the price equal to marginal cost. complete the second row of the previous table. suppose that the government forces the monopolist to set the price equal to average total cost. complete the third row of the previous table. under average-cost pricing, the government will raise the price of output whenever a firm’s costs increase, and lower the price whenever a firm’s costs decrease. over time, under the average-cost pricing policy, what will the local telephone company most likely do