Mr. Robot is a computer repair shop in New York City. The overall inverse demand function for computer repair in New York is P(Q) = 330−3Q, where Q represents the number of computers repaired in NYC per month. Mr. Robot’s cost function is given by C(q) = 15 + 10q + 2q 2 , where q is the total number of computers repaired per month.
1.1.1 Perfect Competition: Suppose there are 20 other computer repair shops who compete with Mr. Robot in a perfectly competitive market. All firms have the same cost function, so the aggregate (i.e., market) total cost function is given byC(Q) = 300+10Q+ 1 10Q2 .
(a) Derive the market marginal cost function (i.e, the market supply curve).
(b) Solve for the competitive market quantity (i.e., total quantity Q) and price (P).
(c) Solve for Consumer Surplus, Producer Surplus and Total Surplus.
1.1.2 Monopoly: Now suppose that E-Corp buys Mr. Robot and the other 19 computer repair shops in NY. Their total cost function is now equal to the aggregate cost function.
(a) Solve for the equilibrium monopoly price (P) and quantity (Q).
(b) Solve for Consumer Surplus, Producer Surplus, Total Surplus and Dead Weight Loss.
(c) Compare the perfectly competitive market to the monopoly.
(d) Suppose that instead of buying all the computer repair shops, the market is still competitive but E-Corp increases the price of parts sold to these repair shops (i.e., increases the marginal cost by a constant). By how much would E-Corp need to increase the price in order for the equilibrium competitive price to be equal to the monopoly price you found in (a).