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

ID: 1195449 • Letter: A

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= 22500-5Q(T)

Apple's Marginal cost function for their mobile phone is:

MC(L)=4450+4.25Q(L)

The overall marginal cost function for the non leaders is

MC(F)=2150+4.5Q(F)

A. if apple wants to maximize profits, how many mobile phone units should they produce? and 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 supply?

Comment: show me the steps to get to the answers please?

Explanation / Answer

Answer: a) Apple is in equilibrium where MR = MC

AR = 22500-5Q

TR = 22500Q-5Q2

MR = 22500-10Q

MR = MC

22500-10Q = 4450-4.25Q

5.75Q = 18050

Q = 3940 units

P = 22500-5Q = 22500- 5(3940) = $6800

Other firms

22500-10Q = 2150-4.5Q

5.5Q = 20350

Q = 3700 units.

22500-9Q =