You are given the following data for your firm, which sells high-capacity video MP3 players.
Q P TC
0 $440 $100
2 $420 $468
4 $400 $788
6 $380 $1084
8 $360 $1380
10 $340 $1700
12 $320 $2068
14 $300 $2508
16 $280 $3044
18 $260 $3700
20 $240 $4500
a. Determine equations for P=f(Q), MR=f(Q), ATC=f(Q, Q2), AVC=f(Q, Q2), MC=f(Q, Q2). Recall that your marginal equations should be derivatives of your totals!
b. Determine the profit-maximizing price and quantity. (Since MC is in terms of Q2, solving with calculus and algebra can be messy. Your table should give an exact answer.)
c. How much total profit would your firm earn if you set P and Q according to part b?
d. Describe the competitiveness of the market by calculating the Lerner index.