Question

PART VI. Problems. Solve the following problems. Please show your work, especially how you calculate a) marginal revenue, the b) profit maximizing quantity and price, c) the Cournot reaction function [best response functions) and the Stackelberg model. (3 points for each problem.) 33. A regulated monopoly faces the following demand for its product, P = 68 - 4Q, and has a marginal cost of MC = 20. Q is the quantity sold and P is the price. a. Under regulation, the firm must set P=MC. Find the regulated price and quantity in this market. b. Suppose the firm is deregulated and therefore sets prices at the monopoly profit-maximizing level. What is equilibrium price and quantity for its product now? c. Now, imagine two firms, competing on quantity, selling the same product, with the same MC = 20. Use this information to find the Cournot solution to both firms' profit maximizing output and price. d. Comparing prices set at marginal cost (a.), prices set at the profit maximizing level (b.) and prices set by profit maximizing oligopolies (c.), where are the prices highest? Lowest? How does the oligopoly prices in c. compare to the other two?

Answer 1

Ans.(33) P= 68-49 mc= 20 regulation optimal conclition P= mc. 68-uo =20 = 68-20=ug = 48 = = Q = 12. P=68-4601 P=68-4 (12) = 68-48= 20. regulated Price P= 20 and quantity as = 12. (b) deregulated from P= 68-49 TR= P. Q = (68-49 la = MR = DTR MR = 68-8 g. optimal conclition MR=mc 68-80 = 20 - 68-20 = 80 = U8 = 80 = Q = us = 6. P= 68-4 (8) = 68-4 (6) = 68-24 = 44. equilibrium Price P=u4 equilibrum quantity &=6.

(C) Coceanot oligopoly. Q = aitqz. mci = mc2 = 20 P= 68-4 (91792). Profit function for Firom - I Ti = TRI- TCI = P.9,- MC.9, = (P-mola, T = (pmc, 19, T = (P-20 )9, - (66-491-492- 2019, T = (48-491-49219, F.o.c di = 48-89, - ua2 = 0 - 48-492 = 9, Best reslonce of from - I (BR) By Symmetry. Q2 = 48-42 Best Responce of from-2. (BR2) Solving BR and BR2 9 = 48-492 8 =) 89, = 48-uar >> 89,-48-4 (48-494) from BR2. om =) 89, = 48-48-422)

- 891 = us-24 +291 =) 69, = 24 - 9 = 24/6 = 4. By using BR-2. a = -3. 48-ual - 8 48-4(u) - 48-16 8 ch there fore q = 92 = 94. P= 168-4 cal - 68-4 (a1 +92) p=68-4 (8) = 6ett 68-32=36 Profit maximizing out furt 9, = 92 =4 and Price P=36. (d) Price set with regulation P= 20 Price set with the regulated P=u4 Price set with oligopoly P=36. Price (regulation) > Price (artigo lay)s plequia ted from ) Highest Price are in unregulated monofoly and lowest in regulated monopolist. oligopoly Price (P= 36) > (regulated from Price = 20) oligopoly Price (P=86) < (unregulated price P= 44).