You are given the following data for your firm, which sells a patented super-absorbent cleaning towel for use in large retail complexes (called "One Wring to Rule the Mall" ).

Q P TC

0 $23.00 $400.00

10 $22.00 $513.00

20 $21.00 $606.00

30 $20.00 $685.00

40 $19.00 $756.00

50 $18.00 $825.00

60 $17.00 $898.00

70 $16.00 $981.00

80 $15.00 $1,080.00

90 $14.00 $1,201.00

100 $13.00 $1,350.00

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.