You are given the following data for your firm, which sells high-capacity video MP3 players. Determine equations for P=f(Q), MR=f(Q), ATC=f(Q, Q 2 ),...

You are given the following data for your firm, which sells high-capacity video MP3 players.

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.

Q P TC

0 $1,000 $1,500

2 $960 $2,568

4 $920 $3,660

6 $880 $4,824

8 $840 $6,108

10 $800 $7,560

12 $760 $9,228

14 $720 $11,160

16 $680 $13,404

18 $640 $16,008

20 $600 $19,020