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Wize AP Microeconomics Textbook > Monopoly

Profit Maximization

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Profit Maximization in a Monopoly

2 Key Assumptions of a Monopoly:

  • Price Setter - a monopoly is when there is only one firm in the industry that has a lot of market power, which means they have a lot of influence over the prices they set (opposite of perfect competition where each firm is a price taker and has no market power).
  • High Barriers to Entry - it is difficult for new firms to enter the market Example: Government doesn't allow new firms to enter or patents for a new medicine.

Profit Maximization

 Marginal Revenue (MR) = Marginal Cost (MC)\boxed{\text\ Marginal\ Revenue\ \left(MR\right)\ =\ Marginal\ Cost\ \left(MC\right)}
  • If Marginal Revenue (MR) > Marginal Cost (MC) , the firm should
    increase
    output
  • If Marginal Revenue (MR) < Marginal Cost (MC) , the firm should
    decrease
    output
  • When MR = MC , profit is
    maximized
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Marginal Revenue

Marginal revenue is the additional revenue from selling one additional unit.
Marginal Revenue (MR)= (ΔTotal Revenue)ΔQ\boxed{\text{Marginal\ Revenue (MR)} =\ \frac{\left(ΔTotal\ Revenue\right)}{ΔQ}}

  • When Total Revenue (TR) is decreasing, the Marginal Revenue (MR) is
    negative
  • When TR is increasing, the MR is
    positive
  • When TR is at its maximum, MR is equal to
    0
    . In the diagram above this is at an output of
    25
    .

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Steps to Find Profit for a Monopoly

  1. Make MR = MC to find profit maximizing output. In the diagram below this is at an output of
    20
  2. Plug that output in the demand to find the price. This is at a price of
    $80
  3. Plug that same output in the ATC. This is at a cost of
    $70
  4. Find profit using the formula Profit = (P - ATC) * Q =
    (80 - 70) * 20 = $200



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Example: Profit Maximization

In the short run, a monopolist with a loss of $50, along with marginal revenue of $20, and marginal cost of $15, should

A) shut down
B) expand output and raise price
C) expand output and cut price
D) cut output and raise price

C
It doesn't matter that they are making a loss. If MR > MC they should increase output. To increase quantity they have to lower the price to get people to buy more.

Practice: Profit Maximization

If a profit-maximizing firm's marginal revenue is less than its marginal cost, the firm


Practice: Marginal Revenue

If the marginal revenue is negative: