1. apple feels it is a price leader in the mobile phone market with all the othe

Question

1. 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 supply?

Explanation / Answer

(A) Total market demand for mobile phones is as follows -

P = 22,500 - 5Q(T)

or,

5Q(T) = 22,500 - P

Q(T) = 4,500 - 0.2P

Marginal cost function of Apple -

MC(L) = 4,450 + 4.25Q(L)

Marginal cost function of Followers -

MC(F) = 2,150 + 4.5Q(F)

Total market demand is as follows -

Q(T) = Q(L) + Q(F) --- (i)

MC(F) = 2,150 + 4.5Q(F)

Q(F) = 478 - 0.22MC(F) --- (ii)

Unde price leadership model, dominant firm act as price maker while followers act as price takers.

So, marginal cost of followers equal the market price.

Putting P in place of MC(F) in equation (ii) -

Q(F) = 478 - 0.22P

Market demand is as follows -

Q(T) = Q(L) + Q(F)

Putting va;lue of Q(T) and Q(F) in above equation to determine demand of Apple [Q(L)] -

4,500 - 0.2P = Q(L) + 478 + 0.22P

Q(L) = 4,022 - 0.42P   ---(iii)

Rearranging equation (iii) to make P as function of Q(L) -

P = 9,576 - 2.38Q(L) --- (iv)

Calculating Total Revenue of Apple -

TR(l) = P * Q(L) = [9,576 - 2.38Q(L)] * Q(L) = 9,576Q(L) - 2.38Q(L)2

Calculating Marginal revenue of Apple -

MR(L) = d(TR(L))/dQ(L) = d(9,576Q(L) - 2.38Q(L)2)/dQ(L) = 9,576 - 4.76Q(L)

Equatin MR and MC of Apple to determine profit maximizing quantity of Apple -

MR(L) = MC(L)

9,576 - 4.76Q(L) = 4,450 + 4.25Q(L)

Q(L) = 569

The profit maximzing quantity of Apple is 569 mobile phones.

Calculating Price by plugging the vale of Q(L) in equation (iv) -

P = 9,576 - 2.38Q(L) = 9,576 - (2.38*569) = 9,576 - 1,354 = 8,222

The price charged by Apple is 8,222.

Thus, if Apple wants to maximize profits, it should produce 569 mobiles and should charge $8,222.

(B) Calculate Total amount of mobile phone demanded in the market at the price set by Apple -

Price set by Apple = $8,222

Q(T) = 4,500 - 0.2P = 4,500 - 0.2 * 8,222 = 4,500 - 1,644 = 2,856

The total mobile phone demanded in the marketv at price set by Apple are 2,856 mobile phones.

Calculate mobile phone supplied by Followers -

Q(F) = Q(T) - Q(L) = 2,856 - 569 = 2,287

The mobile phones supplied by Followers are 2,287 mobile phones.

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