Case 1.1: Profit Maximization and Optimal Pricing with Price Discrimination Scen

Question

Case 1.1: Profit Maximization and Optimal Pricing with Price Discrimination

Scenario: American Airlines (AA) is trying to maximize profits across two kinds of travelers: vacationers (Group A) and business travelers (Group B). AA can effectively distinguish between the two types and can discriminate in pricing. Although fixed costs matter a lot for the calculation of profits, they do not matter for purposes of optimal pricing, so we’ll ignore them for now; however, we cannot ignore marginal costs, which we will assume is a constant $100 per traveler. (For purposes of calculating total profit below, you can assume no fixed costs, for convenience.) Demand for each type of traveler is given by the following equations, where Qi and Pi is the quantity and price for type i:

QA = 1000 – 2PA   QB = 800 – PB

1. If AA must charge the same price to all customers and faces no capacity constraints, what price should it charge, how many tickets will it sell to each customer type, and how much profit will the company make, prior to considering fixed costs?

Show your work here:

Solutions:
Price:
Quantity of type A:
Quantity of type B:
Total Profit:

2. If AA can discriminate between customer types and charge each group a different price, what prices maximize profits now?

Show your work here:

Solutions:
Price to type A:
Price to type B:
Quantity of type A:
Quantity of type B:
Total Profit:

3. Again, assume AA can discriminate as above, but now the airline is constrained by the number of seats available: the maximum number of seats is 300. How should AA adjust to maximize profits?

Show your work here:

Solutions:
Price to type A:
Price to type B:
Quantity of type A:
Quantity of type B:
Total Profit:

Case 1.2: Time Value of Money and Firm Valuation

Smokestack Technologies, Inc. (STI), is a company in a declining industry. The company is currently earning profits of $10 per share of common stock, but the company's profitability is expected to decline by 10% annually forever. The company intends to fully distribute whatever profits are earned to stockholders annually in the form of dividends, beginning with an immediate payment of $10 per share now and continuing payouts on this date each year from now. The relevant interest rate is 10% annually. A popular investors’ newsletter issues a recommendation to sell STI stock at its current price of $47 per share, based on the argument that the stock's value can only go down in the future as its profits decline. Do you agree with the recommendation to sell? Explain.

Show your work here:

Your conclusion:

Explanation / Answer

1. When same price has to be charged then both the demand would be summed up to get aggregate demand as follows -

Q = 1000 – 2P+ 800 – P

Q = 1800 - 3P

or P = 600-Q/3

Now equate MR and MC

MR = dTR/dQ = d(600Q-Q2/3)/dQ = 600- 2Q/3

and MC = 100

then

600 - 2Q/3 = 100

1800 - 2Q = 300

Q = 750

And P = 600-Q/3 = 600 - 750/3 = 350

Now put 350 into QA and QB

QA = 1000 – 2P

QA = 1000- 2(350) = 300

and

QB = 800 - P = 800 - 350 = 450

Total Profit = TR - TC = P*Q - MC(Q) = 350*750 - 100(750) = $187500

2. When it can charge differently then will put MRA = MC and MRB=MC as follows

QA = 1000 – 2PA

so PA = (1000-QA)/2

MRA = dTRA/dQA = d(PA*QA)/dQA = 500-QA

NOW MRA = MC

500-QA=100

QA=400

and PA = (1000-400)/2 = $300

ProfitA= TR - MC(QA) = 300*400 - 100(400) = $80000

SImilarly

Qb = 800 – PB

so PB = (800-QB)

MRB = dTRB/dQB = d(PB*QB)/dQB = 800-2QB

NOW MRB = MC

800-2QB=100

QB=350

and PB = 800-350 = $450

ProfitB= TR - MC(QB) = 450*350 - 100(350) = $122500

Total Profit = $202500

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