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# market demand and asymmetric cost functions

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1. Consider the following market demand and asymmetric cost functions for the airplane production industry.

Market Demand is: P=200- (qA + qB)
Cost Function for Boeing: C(qB) = 40 qB
Cost Function for Airbus: C(qA) = 30 qA

a.) Assume that the two act according to the Cournot model, i.e. they set quantities. Derive the optimal output for each firm and the resulting market price. Be careful with the algebra, as the firms are no longer symmetric.
b.) Suppose now Boeing is the Stackelberg leader. What are the optimal outputs for the two firms and the market price under this assumption?
c.) Suppose now Airbus is the Stackkelberg leader. What are the optimal outputs for the two firms and the market price under this assumption?
d.) Comment on the differences in your answers to (a.)(b.) and (c.). What are the implications of having the higher cost firm as the Stackelberg leader when compared to the Cournot equilibrium? What are the implications of having the lower cost firm as the leader when compared to the Cournot equilibrium?
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https://brainmass.com/math/basic-algebra/market-demand-and-asymmetric-cost-functions-56772

#### Solution Preview

a.) Assume that the two act according to the Cournot model, i.e. they set quantities. Derive the optimal output for each firm and the resulting market price. Be careful with the algebra, as the firms are no longer symmetric.

If both firms set their output levels assuming that the other firm will act like a monopolist with the rest of the market, the outcome is called a Cournot equilibrium.
- Each firm takes the other firm's output as given and chooses the output that maximizes its profits
- The price that emerges clears the market (demand = supply)

ProfitA = PQA - TCA
= (200 - QA - QB) QA - (30QA)
= -QA2 + (170 - QB)QA
by first order condition:
d(ProfitA)/dQA = -2QA + 170 - QB= 0 (1)

ProfitB = PQB - TCB
= (200 - QA - QB) QB - (40QB)
= -QB2 +( 160 -QA)QB
by first order condition:
= d(profitB)/dQB = - 2QB ...

#### Solution Summary

Assess market demand and asymmetric cost functions.

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