Problem
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
|
$160
|
$3,000
|
|
10
|
$152
|
$3,630
|
|
20
|
$144
|
$3,990
|
|
30
|
$136
|
$4,170
|
|
40
|
$128
|
$4,260
|
|
50
|
$120
|
$4,350
|
|
60
|
$112
|
$4,530
|
|
70
|
$104
|
$4,890
|
|
80
|
$96
|
$5,520
|
|
90
|
$88
|
$6,510
|
|
100
|
$80
|
$7,950
|
1. 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!
2. Determine the profit-maximizing price and quantity. (Since MC is in terms of Q2, solving with calculus and algebra can be messy unless you know the quadratic formula. Your table should give an exact answer.)
3. How much total profit would your firm earn if you set P and Q according to part 2?
4. Describe the competitiveness of the market by calculating the Lerner index.