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Refer to Scenario 15.1. A monopolist has total cost TC = Q2 + 10Q + 100 and marginal cost MC = 2Q + 10.  It faces demand Q = 130- P (so its marginal revenue is MR = 130 - 2Q).  Its profit-maximizing output and profit are respectivelyGroup of answer choicesQ=30 and $1,700Q=25 and $ 2,500Q=20 and $450Q=10 and $1,300

Question

Refer to Scenario 15.1. A monopolist has total cost TC = Q2 + 10Q + 100 and marginal cost MC = 2Q + 10.  It faces demand Q = 130- P (so its marginal revenue is MR = 130 - 2Q).  Its profit-maximizing output and profit are respectivelyGroup of answer choicesQ=30 and 1,700Q=25and1,700Q=25 and 2,500Q=20 and 450Q=10and450Q=10 and 1,300

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Solution

To find the profit-maximizing output for a monopolist, we need to set Marginal Cost (MC) equal to Marginal Revenue (MR) and solve for Q.

Given MC = 2Q + 10 and MR = 130 - 2Q, setting these equal to each other gives:

2Q + 10 = 130 - 2Q

Solving for Q gives Q = 30.

To find the profit, we first need to find the price that the monopolist will charge at this quantity. We can do this by substitifying Q = 30 into the demand equation Q = 130 - P:

30 = 130 - P

Solving for P gives P = 100.

The total revenue (TR) is then PQ = 10030 = $3000.

The total cost (TC) at Q = 30 is Q^2 + 10Q + 100 = 30^2 + 10*30 + 100 = $1300.

So, the profit (π) is TR - TC = 30003000 - 1300 = $1700.

Therefore, the profit-maximizing output and profit are Q=30 and $1,700.

This problem has been solved

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