Chapter 11: Answers to Questions and Problems
1.
a. Since E = EF = EM, .
b. .
c. .
2. x
a. P = $60, Q = 4, and profits = 4($60 – $20) = $160.
b. Charge the maximum price on the demand curve starting at $100 down to $20 for each infinitesimal unit up to Q = 8 units. Profits are 8($100 – $20)(.5) = $320.
c. Charge a fixed fee of $320 and a per-unit charge of $20 per unit to earn total profits of $320.
d. Create a package of 8 units and sell the package for $480. Total profits are $320.
3.
a. Second-degree price discrimination.
b. $8 + 2($4) = $16.
c. Total profits under perfect price discrimination are 5($18 – 8)(.5) = $25, so this strategy would lead to an extra $9.
4.
a.  and .
b. Here, there are two different groups with different (and identifiable) elasticities of demand. In addition, we must be able to prevent resale between the groups.
5.
a. Charge a fixed fee of $160, plus a per-unit charge of $20 per unit.
b. The optimal per-unit price is determined where MR = MC, or 100 - 40Q = 20. Solving yields Q = 2 units and P = $60. The profits at this output and price are $120 - $40 = $80. Thus, you earn $80 more by two-part pricing.
6.
a. The inverse demand function is P = 200 – 4Q. Marginal cost is $120. The optimal number of units in a package is that output where price equals marginal cost. Thus we set 200 – 4Q = 120 and solve to get the optimal number of units in a package, Q = 20 units.
b. The total value to a consumer of the 20 units, which is $3,200 (computed as (.5)(20)($200 - $120) + ($120)(20) = $3,200).
7.
a. $225,000 (since all consumers purchase each product, you earn $75,000 on sales of good X and $150,000 on sales of good Y).
b. $200,000 (since only the highest valuation type purchases each product, you earn $60,000 on sales of good X and $140,000 on sales of good Y).
c. Since all consumers receive at least $110 in value from the bundle, all types buy the bundle. Profits are thus $330,000....