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Answer to Question #71169 in Macroeconomics for nurain

Question #71169
ALCHEM (L) is a price leader in the polyglue market. all 10 other manufacturers (follower (F) Firms) sell polyglue at the same price as ALCHEM. Alchem allows the other firms to sell as much as they wish at the establish price by the following function (QT=QL+QF):

P=10,000-10QT

ALCHEM'S marginal cost function for manufacturing and selling polyglue is:
MCL=100+3QL

the agregate marginal cost function for the other manufacturers of polyglue is:
∑MCF=50+2QF

A) to maximise profits how much polyglue should Alchem produce and what price should it charge

B) what is the total market demand for polyglue at the price established by alchem in part (A)? how much of total demand do follower firms supply?
Expert's answer
QT = QL + QF, P = 10,000 - 10QT,
MCL = 100 + 3QL, ∑MCF = 50 + 2QF.
A) to maximise profits Alchem should produce at MR = MC,
MR = TR' = (P*Q)' = 10,000 - 20QT,
10,000 - 20Q = 100 + 3Q,
23Q = 9,900,
Q = 430 units.
P = 10,000 - 10*430 = $5,700.
B) The total market demand for polyglue at the price established by alchem in part (A) is:
5,700 = 10,000 - 10QT,
10QT = 4,300,
QT = 430 units.

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