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)

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

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 supply?

Explanation / Answer

market dd curve : P = 22500-5Q or Q = 4500 - P/5

Fring firms' supply curve (derived from their marginal cost surve) : Qa= P/4.5 - 21500/45

Apple's demand curve = market dd curve - fringe firms' ss curve : Qa = 4977.77 - 19P/45 or P = 11789.5 - 2.37Qa

total revenue of Apple = P*Qa = 11789.5Qa - 2.37Qa2

MR = d/dQa = 11789.5 - 4.7Qa

profit maximizing condition for Apple : MC = MR

4450 +4.25Qa = 11789.5 - 4.74Qa

Qa = 815.5 = 816

P = 9857

Total market demand at (P=9857) = 4500 - 9857/5 = 2528

Supply by followers = P/4.5 - 21500/45 = 9857/4.5 - 21500/45 = 2189.1 - 477.8 = 1711

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