Question

answer parts a-d. show all work.

1. Suppose you are a monopolist facing the following demand curve: PD 200-5Q Further assume you have the following cost structure: C() 5+100+ 100 Given these formulas, please answer the following questions: a. What is the profit-maximizing price and quantity? How profit does this yield? Full credit answers will verify that Q relates to a profit maximum and show all work. (5 pts) b. What is the socially efficient price and quantity? How much profit does this combination generate for the firm? Show work. (5 pts) c. Graph this scenario and compute the total amount of DVWL (if any) generated by the market outcome. Be sure to include/label a demand curve, average total cost curve, marginal revenue curve, marginal cost curve, (Qmax Pmax), ATCmax (soc Poc) and the firms profit rectangle. (5 pts) d. Verify that the profit maximizing price derived in part "a." is the same price as you would get using the Lerner Index to compute P".(5 pts)

Answer 1

all Monopoly at Eqm MR = 200-100, Mc= dc = 10 + 200 MR = MC 200-100=10+200 190=300 Q' - (190)/30 = 6-33 P= 200-5(19) - $168.33 Ang n = TR-TC (6.33)2 = (633) (168.33) 5-10(6.33) - 10 = 1065.55 - 5 - 63.3-400.689 π = $596.561 Ans 6. Now at socially efficient Eqm P=MC. 200-50 = 10+20Q 190=25 Q & Q =706 pl=200-58' - $162 Ang T = TR-TC = (162) (7.6) - 5-10 ( 706) - 10 (7.6) 2. = 1231.2- 5-46-541.6 = $572.6 And c) Graph , ATC= TE = 5 +104 10Q DWLE *[Q'-Qv). [168-33-162) = 19[7.6-6.33] [6.33) = 4 $ Ans [ at Q=7.6 MC=10+20x706 = 162]

800 PMC HATC. max 4 Rectangle of Profit -- lo TMR HQI SOL 40 Q7 MONDO