Managerial Economics Applications, Strategies and Tactics 14th Edition by James SM
Pricing Techniques and Analysis
Solutions to Exercises
1. Using the formula given below to calculate differential prices of textbooks in two separate markets:
P (1 + (1/Ed)) = MR = MC.
U.S. market Overseas market
P (1 + (1/2)) = 40 P (1 + (1/3)) = 15
P = $80/unit P = $22.5/unit
2. Optimal price discrimination would equate the derived MR in each market equal to the marginal cost i.e. $120. MR is derived using the formula:
P (1 + (1/Ed)) = MR.
The subscripts represent 1 for 1st class, c for coach, and d for discount:
P1 (1 + 1/−1.3) = Pc (1 + 1/−1.4) = Pd (1 + 1/−1.9) = $120
P1 (−0.3/−1.3) = Pc (−0.4/−1.4) = Pd (−0.9/−1.9) = $120
P1 (+0.231) = Pc (+0.285) = Pd (+0.474) = $120
Solving each of the above equations: P1= $519, Pc = $421, and Pd = $253
3. Two classes of freight of the American export-import shipping company:
a. Demand functions: P1 = 100 2Q1 for manufactured goods and P2 = 80 Q2 for semi-manufactured raw materials.
Revenue function: TR = (100 Q1 – 2 Q12) + (80 Q2 – Q22)
Cost function: TC = 20 + 4(Q1 + Q2)
Profit function: = TR − TC = 20 + 96Q1 + 76Q2 2Q12 Q22
b. Solving for the profit-maximizing levels of price and output for both freight categories: ∂/∂Q1 = 96 4Q1 = 0 and /Q2 = 76 2Q2 = 0
Q1* = 24 tons; P1* = $52/unit and Q2* = 38 tons; P2* = $42/unit
c. TR = 100Q1 2Q12 + 80Q2 Q22
MR1 = (TR)/Q1 = 100 4Q1 = 100 4(24) = $4
MR2 = (TR)/Q2 = 80 2Q2 = 80 2(38) = $4
d. * = 20 + 96(24) + 76(38) 2(24)2 (38)2 = $2,576
e. Under uniform pricing, P1 = P2 = P
100 2Q1 = 80 Q2
Q2 = 20 + 2Q1
= 1940 + 328Q1 6Q12
Solving for profit-maximizing price and output levels: d/dQ1 = 328 12Q1 = 0
Q*1 = 27.3 tons, Q*2 = 20 + 2(27.3) = 34.6tons
Q* = 27.3 + 34.6 = 61.9 tons
P* = 100 2(27.3) = $45.4/unit
* = (45.4) (61.9) 20 4(61.9) = $2,542.66
Profit is higher when the firm is permitted to use differential pricing.
f. E1 = Q1/P1 P1/Q1 , E2 = Q2/P2 P2/Q2
Q1/P1 = 1/2, Q2/P2 = 1
Using the uniform prices and quantities:
E1 = .5(45.4/27.3) = 0.83 (inelastic), E2 = 1(45.4/34.6) = 1.3 (elastic)
The lower the price elasticity, i.e., the lower the |Ed|, the higher is the price charged. Accordingly, in (b) above, P1 = $52 and P2 = $42. Hence, we sell at a price in region one that is the inelastic portion of the demand curve foregoing potential profits.
4. →Pay-per-view movies on cable TV are priced with typically user charges only, but some require a monthly payment that makes it two-part pricing.
→Pay phones are priced with user charges only.
→Netflix is priced with a monthly lump sum fee (with a maximum number of movies per download).
→iTunes are priced with user charges only.
→Country club memberships are often two-part pricing: annual membership fee plus additional fee for services (sometimes with a required minimum purchase per month).
→Soda from a vending machine is priced with user charges only.
→Laundromats are priced with user charges only.
→Season ticket holders with seat rights are priced with two-part pricing, with the ‘seat rights’ as a form of membership fee and the price of the tickets in the block booking as the price of each item. User charges would technically be game-specific and block booking of a season’s passes is a lump sum entry fee.
5. Revenue functions for Phillips Industries: TR1 = P1∙Q1 = (60 2Q1)∙Q1 = 60Q1 2Q12 ,and
TR2 = P2∙Q2 = (40 − Q2)∙Q2 = 40Q2 – Q22
Cost function: TC = 10 + 8Q1 + 8Q2
= TR TC = 10 + 52Q1 2Q12 + 32Q2 Q22
b. Solving for profit-maximizing levels of output in the two markets: /Q1 = 52 4Q1 = 0 and /Q2 = 32 2Q2 = 0
Hence, Q1* = 13 units; P1* = 60 2(13) = $34/unit and Q2* = 16 units; P2* = 40 16 = $24/unit
c. TR1 = 60Q1 2Q12 and MR1 = 60 4Q1 = 60 4(13) = $8
TR2 = 40Q2 Q22 and MR2 = 40 2Q2 = 40 2(16) = $8
d. * = 10 + 52(13) 2(13)2 + 32(16) (16)2 = $584
e. If P1 = P2,
60 2Q1 = 40 Q2
Q2 = 2Q1 20
= 1050 + 196Q1 6Q12
Solving for profit-maximizing price and output levels: d/dQ1 = 196 12Q1 = 0
Q1* = 16.333 units and Q2* = 2(16.333) 20 = 12.667 units
Q* = 16.333 + 12.667 = 29 units
P* = 60 2(16.333) = $27.33/unit
* = 1,050 + 196(16.333) 6(16.333)2 = $550.67
a. One of the reasons why universities may charge different prices for different courses is the different costs of production involved in each course (for example, compare business to religious studies). A mass lecture on world religions is less expensive than a seminar on consolidations in accounting. Students have different demand functions for various courses of study that may also promote different pricing. Everyone expects a med school to be more expensive than a grad school that offers different courses in foreign languages. If the demand is higher, prices may be set higher. Presumably, demand for various courses of study will reflect rates of return expected to be earned by those who undertake these courses of study.
b. Assuming that students in those disciplines where the cost of providing education is highest also receive the largest lifetime income benefits from their education, the practice of charging the same fee to all students discriminates against those students who do not choose the high cost, high return disciplines. For example, one would suspect that students in the social sciences and humanities are subsidizing students in the sciences, engineering, and the professions.
c. Many of the high cost disciplines would probably receive less emphasis, at least in terms of demand from students. We might find low enrollment in departments like geography, classics, or Portuguese. At the same time, students from low income families might be precluded from the sciences professions unless significant financial aid is provided.
d. Faculty members might be utilized more intensively by teaching larger sections. Small classes, where the cost is high, would become even more of a luxury than they are today. Low demand, high cost majors might be eliminated. [Actually, this is happening.]
e. Forecasting the size of a class would be essential in order to set different pricing for different courses of study. It would be a challenge to meet the needs of students with lower income who cannot afford the high cost (high return) disciplines.
7. General Medical makes disposable syringes for hospitals and doctor supply companies.
a. Contribution for Defense Department order: AVC = 1.20/1.5 = 80 cents
= 300,000(20 cents contribution from the Defense Department order) less the lost contribution from the forgone sales to regular customers i.e. (100,000)(40 cents contribution from the forgone sales to regular customers) = $60,000 $40,000 = +$20,000. Therefore, they should accept the order.
b. If General Medical accepts the Defense contract, the cost of the additional lost sales would be: $50,000(40 cents) = $20,000. Under these conditions, the firm will be indifferent.
8. a. Demand function: P= 2,500 .0005Q
MC = $900
Revenue function: TR = P∙Q i.e., TR = 2,500Q .0005Q2
The profit-maximizing level of output occurs where MR = MC.
Therefore, MR = 2,500 .001Q = $900
Q* = 1,600,000 units and P* = 2,500 .0005(1,600,000) = $1,700/unit
b. Profit contribution = 1,700(1,600,000) 900(1,600,000) = $1,280,000,000
c. Time Period PRICE(Q) COST(Q) CONTRIBUTION
1 Profit contribution = 2,400(200,000) 900(200,000) = $300,000,000
2 Profit contribution = 2,200(200,000) 900(200,000) = $260,000,000
3 Profit contribution = 2,000(200,000) 900(200,000) = $220,000,000
4 Profit contribution = 1,800(200,000) 900(200,000) = $180,000,000
5 Profit contribution = 1,700(200,000) 900(200,000) = $160,000,000
6 Profit contribution = 1,600(200,000) 900(200,000) = $140,000,000
7 Profit contribution = 1,500(200,000) 900(200,000) = $120,000,000
8 Profit contribution = 1,400(200,000) 900(200,000) = $100,000,000
9 Profit contribution = 1,300(200,000) 900(200,000) = $ 80,000,000
10 Profit contribution = 1,200(200,000) 900(200,000) = $ 60,000,000
Total is: $1,620,000,000
d. Total profit contribution under the price skimming strategy is $1,620,000,000 compared with $1,280,000,000 under the simple monopoly pricing scheme in part b.
e. The major advantage is the higher profit level. The major problems are deciding when to make the price cuts, how to schedule the production, and the higher potential for competitive intervention.
Case Exercise: Partitioning the price of the Chevy Volt
1. Life cycle cost includes the cost of acquisition, training, maintenance, upgrades, and disposal. Given the depreciation rate of an electric vehicle i.e. 22 percent per year, the maintenance and the disposal cost will increase at year 5.
Yes, with high life cycle cost the resale value of an electric vehicle at year 5 would be very low. Value-in-use is the difference between the value customers place on function, cost savings, and relationships attributable to a product or service and the life cycle costs of acquiring, maintaining, and disposing of the product or service. With an increase in the life cycle cost, the perceived value-in-use would fall.
2. Under the policy of high fixed residual in closed-end lease of battery pack, the entire depreciation risks and costs would be solely borne by Chevrolet. This would increase the credibility about the performance of the battery because the consumer will know that if any damage happens to the battery pack within the terms of the lease, Chevrolet will pay for the damage. However, a closed-ended lease would also give more control to Chevrolet over the consumer’s use and thereby, avoid any extra payment for the damages that would result from inappropriate use of the vehicle by the consumer. In contrast, by issuing a 10-year warranty the company loses control over the consumer’s use and may end up paying more if the damage to the battery results from inappropriate use or carelessness by the consumer.
3. If Chevy bundles the maintenance contracts into the final purchase price, both the direct fixed costs, such as maintenance cost, as well as the indirect fixed costs would be added to variable costs to arrive at the final price. The final value of the vehicle would increase by including the maintenance cost in the final price. Therefore, it would lead to more revenue for Chevrolet. Since emergency roadside assistance is an important function or attribute of buying an automobile, Chevrolet may consider including a part of its cost to provide this service in the final purchase price of the automobile.
4. In the possible two scenarios when the seller does not control the imposition of the
expense, and when emergency roadside assistance is not pivotal to the consumer’s
primary benefit, partitioning price practice for emergency roadside assistance can be