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Monopoly single-price: Price & output decisions

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Intros
Lessons
  1. Monopoly Single-Price: Price & Output Decisions Overview:
  2. Maximizing Profit with Total Revenue & Total Cost
    • Use a Table to Keep Track of Information
    • Calculate Total Revenue & Cost
    • Calculate Profit
    • Find the One with the Highest Profit
  3. Maximizing Profit with MR = MC
    • Graphically: Graph MR, MC, ATC and Demand
    • Find the intersection of MR and MC
    • Algebraically: Find equations and set MR = MC
    • Solve and find q and p
    • Find the Economic profit
  4. Deadweight Loss in Single-Price Monopoly
    • Monopoly is inefficient
    • Consumer & Producer Surplus
    • Deadweight Loss
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Examples
Lessons
  1. Graphically Maximizing Profit
    Consider the following graph:

    Maximizing Profit
    1. Find the output and price which maximizes profit.
    2. Find the economic profit.
  2. Consider the following graph:

    Maximizing Profit
    1. Find the output and price which maximizes profit.
    2. Find the economic profit.
  3. Algebraically Maximizing Profit
    Consider the following formulas:

    p = 100 - 4q
    MC = 50 + 2q
    1. Find MR.
    2. Find the output and price which maximizes profit.
  4. Consider the following formulas:

    p = 60 - 2q
    MC = 20 + q
    1. Find MR.
    2. Find the output and price which maximizes profit.
  5. Finding the Deadweight Loss, Consumer Surplus, & Producer Surplus
    Consider the following graph:
    Finding the Deadweight Loss, Consumer Surplus, & Producer Surplus
    1. Calculate the deadweight loss.
    2. Calculate the consumer surplus.
    3. Calculate the producer surplus.
  6. Consider the following functions:

    p = 2 - 2q
    MC = 2q
    1. Calculate the deadweight loss.
    2. Calculate the consumer surplus.
    3. Calculate the producer surplus.
Topic Notes
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The monopoly sets their output and price at a point in which it maximizes economic profit. There are two ways to do this:

Maximizing Profit with Total Revenue & Total Cost

Suppose we know the demand for the product, and the total cost of producing them. Then we can:
  1. Draw a table with the following columns: quantity, price, total revenue, total cost and profit.
  2. Calculate the total revenue ( p × q ).
  3. Calculate the profit (P = R - C ).
  4. Find the output with the highest attainable profit.

Price

(p)

Quantity demanded

(q)

Total Revenue

( R = p × q )

Total Cost

(C)

Profit

(P = R - C)

10

0

0

5

-5

9

1

9

7

2

8

2

16

10

6

7

3

21

14

7

6

4

24

19

5

5

5

25

25

0


In this case, the highest attainable profit when the output produced is 3, the price is $7.

If we graph total revenue and total cost in a graph, then the highest attainable profit will be the output in which TR and TC have the biggest gap.

Monopoly: Maximizing profit with total revenue & total cost

Maximizing Profit with MR = MC

Just like in perfect competition, monopolist find the output q and price p that maximizes profit by solving for MR = MC.

To solve p and q graphically, we do the following:
  1. Graph the MR, MC, ATC, and demand Curve
  2. Find the intersection point of MR and MC to find output q
  3. Use output q to find price p on the demand curve.

Monopoly: Maximizing profit with marginal revenue & marginal cost

To solve p and q graphically, we do the following:
  1. Define formulas for demand curve, MR and MC
  2. Set MR = MC and solve for output q
  3. Put output q into the demand formula and solve for p

To calculate economic profit, we find the average total cost ATC at the output q, and use the formula

Economic Profit = (p - ATC) q

Deadweight Loss in Single-Price Monopoly

Unlike perfect competition, monopolist is inefficient because it creates deadweight loss.

Monopolist produces the output that maximizes profit, but there is a shortage because consumers want more of the product.

Deadweight Loss in single-price monopoly

Note 1: The deadweight loss and consumer surplus can be calculated by using the area of the triangle formula
A = bh2\large \frac{bh}{2}

Note 2: The producer surplus can be calculated by breaking apart the surplus into a triangle and square. Then calculate the areas of each to find the sum.