# Monopoly single-price: Price & output decisions

##### Intros

###### Lessons

**Monopoly Single-Price: Price & Output Decisions Overview:**__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

__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

- Graphically: Graph
__Deadweight Loss in Single-Price Monopoly__- Monopoly is inefficient
- Consumer & Producer Surplus
- Deadweight Loss

##### Examples

###### Lessons

**Graphically Maximizing Profit**

Consider the following graph:

- Consider the following graph:

**Algebraically Maximizing Profit**

Consider the following formulas:*p*= 100 - 4*q**MC*= 50 + 2*q*- Consider the following formulas:
*p*= 60 - 2*q**MC*= 20 +*q* **Finding the Deadweight Loss, Consumer Surplus, & Producer Surplus**

Consider the following graph:- Consider the following functions:
*p*= 2 - 2*q**MC*= 2*q*

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###### Topic Notes

__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:

- Draw a table with the following columns: quantity, price, total revenue, total cost and profit.
- Calculate the total revenue (
*p × q*). - Calculate the profit (
*P = R - C*). - Find the output with the highest attainable profit.

(p) |
(q) |
( R = p × q ) |
(C) |
(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.

__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*.

*, we do the following:*

**To solve p and q graphically**- Graph the
*MR*,*MC*,*ATC*, and demand Curve - Find the intersection point of
*MR*and*MC*to find output*q* - Use output
*q*to find price*p*on the demand curve.

*, we do the following:*

**To solve p and q graphically**- Define formulas for demand curve,
*MR*and*MC* - Set
*MR*=*MC*and solve for output*q* - 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.

Note 1: The deadweight loss and consumer surplus can be calculated by using the area of the triangle formula

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.

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