1. 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	$48.00	$400.00
10	$46.50	$707.50
20	$45.00	$980.00
30	$43.50	$1,232.50
40	$42.00	$1,480.00
50	$40.50	$1,737.50
60	$39.00	$2,020.00
70	$37.50	$2,342.50
80	$36.00	$2,720.00
90	$34.50	$3,167.50
100	$33.00	$3,700.00

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.