Purchase Solution

# Profit Maximization / Product

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While Boeing and Airbus make airplanes, GE, Rolls Royce, and Pratt & Whitney make jet engines. Airlines make their deals with the aircraft manufactures on the aircraft they want and then make a deal with the engine manufacturers with respect to the engines for that aircraft.

Suppose that Boeing decided that it wished to manufacture jet engines by creating an upstream engine division. If they did so, suppose that Airbus would never purchase a Boeing engine.

The demand for Boeing two engine aircraft is estimated as

PA = 30 - QA

where QA is the quantity of Boeing two engine aircraft demanded when the price of a Boeing two engine aircraft is PA.

Boeing's cost of constructing and selling a two engine aircraft (exclusive of the cost of the engines) is:

TCA = 0.5 + 0.05QA + 0.1QA2

where QA is the quantity of two engine aircraft that Boeing makes and sells.

The cost of making a package of two engines in Boeing's upstream engine division is:

TCE = 0.5 + 0.05QE + 0.05QE2

where QE is the quantity of two engine packages that Boeing's upstream engine division makes. It takes one two engine package to make one two engine aircraft.

Suppose that corporate Boeing in Chicago mandates that Boeing's aircraft manufacturing division purchase all engines from Boeing's engine making division.

How many two engine aircraft will Boeing manufacturing, how many packages of two engines will Boeing's engine division manufacture and what price should the aircraft manufacturing division pay to the engine manufacturing division for an engine package?

The aircraft manufacturing division should make _____________ two engine aircraft

The engine manufacturing division should make ____________two engine packages

The aircraft manufacturing division should pay the engine manufacturing division _____ for each two engine package

Suppose now that given the intense competition among GE, Rolls Royce, and Pratt &
Whitney that Boeing could purchase a two engine package on the market for 1.25.
What was the cost to Boeing of pursuing a dedicated engine manufacturing subsidiary? Fractional aircraft can be produced.

The cost of Boeing of pursuing a dedicated engine manufacturing subsidiary is ______ Because the numbers are meant to reflect millions, carry your calculations to at least 4 decimal places.

##### Solution Summary

The expert applies the profit maximization and product usage.

##### Solution Preview

From the demand function: Pa = 30 - Qa
we can write the Total Revenue function: TR=Pa*Qa=(30 - Qa)*Qa=30 Qa - Qa^2
then Marginal Revenue is: MR=dTR/dQa =30 - 2Qa

from the cost function (adding the cost of the engines at unit price Pe):
TCA = 0.5 + 0.05QA + 0.1QA2 + Pe*Qa
the marginal cost is MC=dTCa/dQa = 0.05+ Pe + 0.2QA

to maximize the profit, the firm will choose to produce at MC=MR
i.e. 30 - 2Qa = 0.05+ Pe + 0.2Qa (1)

From the cost of engine division: TCE = 0.5 + 0.05QE + 0.05QE2
MC= dTCE / dQE = 0.05 + 0.1QE
...

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