Question

6. Some personal computer software is sold at special discounts to students. Other software is provided in a less powerful version for students. Why do publishers offer discounts to students? What is the purpose of developing less powerful editions?

7. Using the kinked demand model, explain why a decrease in costs might not lead to a change in price or output (see Chapter 10).

10. Stargazer Recordings sells compact discs in two markets. The marginal cost of each disc is $2. Demand in each market is given by Q1 = 40 – 10P1 and Q2 = 40 – 2P2 where Q is thousands of compact discs.

a. If the firm uses price discrimination, how much output should it produce and what price should it charge? What is its profit? What type of price discrimination is it using?
b. If the firm cannot prevent resale of compact discs, what will its profit be?

Answer 1

6. Some personal computer software is sold at special discounts to students. This is done to increase profits by selling students at a lower price and others at a higher price. Students are more price sensitive so they are likely to buy more if prices are reduced. This is a type of price discrimination.

Other software is provided in a less powerful version for students so that consumers can be lured for a powerful version that priced very high. Discriminating firms realize that if they offer a powerful version only fewer students would buy but if a cheaper version is sold first, students may get habitual and demand a more powerful version of the software which will make demand inelatic. Firms then can charge a higher price once demand is made price inelastic.

7. In kinked demand model, a decrease in costs might not lead to a change in price or output because at the kink there is a discontinuity in the marginal revenue which allows marginal cost to increase in a range without affecting the output.

10. Stargazer Recordings sells compact discs in two markets. The marginal cost of each disc is $2. Demand in each market is given by Q1 = 40 – 10P1 and Q2 = 40 – 2P2 where Q is thousands of compact discs. Inverse demand functions are P1 = 4 - 0.1Q1 and P2 = 20 - 0.5Q2

a. If the firm uses price discrimination, this will be third degree price discrimination where the optimal rule is MR1 = MC and MR2 = MC

4 - 0.2Q1 = 2 20 - 0.5Q2 = 2

Q1 = 10000 units Q2 = 36000 units

P1 = $3 P2 = $5

Profit 1 = (3 - 2)*10 = $10000 Profit 2 = (5 - 2)*36 = $108000

Total profit = 118000
b. If the firm cannot prevent resale of compact discs, it charges a single price. Demand is Q = Q1 + Q2 = 40 – 10P1 + 40 – 2P2 or 80 - 12P1. Inverse demand is P1 = (80/12) - (1/12)Q

Use MR = MC

80/12 - 2/12Q = 2

Q = 28000 units

price P =  (80/12) - (1/12)*28 = 4.33

Profit = (4.33 - 2)*28000 = 65240.