Suppose a company has a monopoly on a game called Monopoly and faces a demand cu

Question

Suppose a company has a monopoly on a game called Monopoly and faces a demand curve given by Qt = 100-P and a marginal revenue function given by MR = 100 - 2QT where QT equals the combined total number of games produced per hour in the company's two factories (QT = Q1 + Q2). If factory 1 has a marginal cost function given by MC1 = Q1 - 5 and factory 2 has a marginal cost function given by MC2 = O.5Q2 - 5, how much total output will the company choose to produce and how will it distribute this production between its two factories in order to maximize profits?

Explanation / Answer

Since company is monopoly, profit maximizes at MC = MR

For Factory 1,

MR=MC1

100 - 2(q1+q2) = q1 - 5

Solving this, 3q1+2q2=105 ............(1)

For Factory 2,

MR= MC2

100-2(q1+q2)= 0.5q2 - 5

solving this, 2q1 + 2.5q2 = 105 ...................(2)

Solving eq(1) and eq(2), we get

q1= 15, q2= 30

Total output, Q=q1+q2= 45

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