# Monopoly single-price: Price & output decisions #### Everything You Need in One Place

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###### 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
##### Examples
###### Lessons
1. Graphically Maximizing Profit
Consider the following graph: 1. Find the output and price which maximizes profit.
2. Find the economic profit.
2. Consider the following graph: 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: 2. Calculate the consumer surplus.
3. Calculate the producer surplus.
6. Consider the following functions:

p = 2 - 2q
MC = 2q
2. Calculate the consumer surplus.
3. Calculate the producer surplus.
###### Topic Notes
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. 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. 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 A = $\large \frac{bh}{2}$