Apple feels it is a price leader in the mobile phone market with all the other p

Question

Apple feels it is a price leader in the mobile phone market with all the other producers acting as followers. The total demand for mobile phones is given as,

P=22,500-5Q(T)

Apple’s Marginal cost function for their mobile phone is, MC(L)= 4,450+4.25Q(L)

The overall marginal cost function for the non leaders is MC(F)= 2,150+ 4.5Q(F)

A. If Apple wants to maximize profits, how many mobile phone units should they produce? How much should they charge?

B. What is the total amount of mobile phones demanded in the market at the price Apple set in the previous question? How many do the followers

Explanation / Answer

Q(T) = QL + QF

A) R1 = P*QL = 22500QL - 5QL^2 - 5QLQF so MR1 = dR/dQL = 22500-10QL-5QF = 0 SO QL=2450-QF/2

R2 = P*QF = 22500QF - 5QF^2 - 5QLQF so MR2 = dR/dQF = 22500-10QF-5QL = 0 SO QF=2450-QL/2

to maximize profit MC = MR

QL = 2450-1/2(2450-QL/2) = 1225 -QL/4 SO QL = 980 AND QF = 980 So QT = 1960

P = 22500-5*1960 = 12700

B. At THIS PRICE QT = 1960

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