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" ©)

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 $19.00 $200.00

10 $18.00 $295.00

20 $17.00 $372.00

30 $16.00 $437.00

40 $15.00 $496.00

50 $14.00 $555.00

60 $13.00 $620.00

70 $12.00 $697.00

80 $11.00 $792.00

90 $10.00 $911.00

100 $9.00 $1,060.00

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.