Suppose that the fixed costs of 0.72 consist of an attributable fixed cost for good 1 of 0.12, an attributable cost of 0.12 for good 2, and a common fixed cost of 0.48. Are the Ramsey prices subsidy free?
Suppose that there are two products. The demand function for good i is Qi = 1 − bi Pi where b1 = 1 and b2 = 0.5. There are no variable costs of production, but there is a common fixed cost equal to 0.72.
(a) Show that the inverse demand
(b) Let W = CS1(Q1) + CS2(Q2). Then iso-welfare contours are combinations of Q1 and Q2 that give the same level of W. Graph three iso-welfare contours in Q1, Q2 space.
(c) Write the firm’s zero-profit constraint in terms of Q1 and Q2. Sketch the firm’s zero-profit constraint in Q1, Q2 space.
(d) Using (b) and (c), graphically derive the quantities that maximize W subject to the firm breaking even. What two characteristics distinguish the Ramsey quantities from any other quantities?
(e) The slope of the iso-welfare contours is dQ2/dQ1=−Q1/2Q2.
The slope of the zero-profit constraint is dQ2/dQ1=−(1 − 2Q1)/(2 − 4Q2).
Find the Ramsey quantities, prices, and W.
(f) Suppose that the regulator determines prices by setting
(i) α = 0.325.
(ii) α = 1/3.
(iii) α = 0.345.
(g) For each of the three cases in (f) determine W and compare it to the Ramsey optimum.
Compare the prices found in the three cases with the Ramsey prices and verify that Ramsey pricing increases W by decreasing the price of the relatively elastic good and increasing the price of the relatively inelastic good.
(h) Suppose that the fixed costs of 0.72 consist of an attributable fixed cost for good 1 of 0.28, an attributable cost of 0.24 for good 2, and a common fixed cost of 0.20. Demonstrate that there is an incentive for inefficient bypass at the Ramsey prices.
(i) Suppose that an entrant captures all of the market for good 2 and charges the Ramsey price. What is the incentive for the incumbent to continue to produce good 1? What is total surplus in the long run? Why was entry inefficient?
(j) Suppose that the fixed costs of 0.72 consist of an attributable fixed cost for good 1 of 0.12, an attributable cost of 0.12 for good 2, and a common fixed cost of 0.48. Are the Ramsey prices subsidy free?
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