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 $26.00 $180.00

10 $25.25 $288.00

20 $24.50 $395.00

30 $23.75 $504.00

40 $23.00 $618.00

50 $22.25 $740.00

60 $21.50 $873.00

70 $20.75 $1,020.00

80 $20.00 $1,184.00

90 $19.25 $1,368.00

100 $18.50 $1,575.00

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.