You are given the following data for your firm, which sells the only toothpick maker for at-home use (called "You CAN handle the tooth(pick)" ).

Q

P

TC

0

$39.80

$400.00

10

$37.30

$546.00

20

$34.80

$692.00

30

$32.30

$850.00

40

$29.80

$1,032.00

50

$27.30

$1,250.00

60

$24.80

$1,516.00

70

$22.30

$1,842.00

80

$19.80

$2,240.00

90

$17.30

$2,722.00

100

$14.80

$3,300.00

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.