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.