Tom Gruszka (Mathematics)Economics: Butter Problem
- The Inverse Demand Curve:
Quantity of Butter (Per Capita, Per Year) |
Price (Per Pound) |
0 |
$10.1992 |
0.25 |
$9.7137 |
0.5 |
$9.2282 |
0.75 |
$8.7427 |
1 |
$8.2572 |
1.25 |
$7.7717 |
1.5 |
$7.2862 |
1.75 |
$6.8007 |
2 |
$6.3152 |
2.25 |
$5.8297 |
2.5 |
$5.3442 |
2.75 |
$4.8587 |
3 |
$4.3732 |
3.25 |
$3.8877 |
3.5 |
$3.4023 |
3.75 |
$2.9168 |
4 |
$2.4313 |
4.25 |
$1.9458 |
4.5 |
$1.4603 |
4.75 |
$0.9748 |
5 |
$0.4893 |
5.25 |
$0.0038 |
- Given the relationship between price and per capita butter demand as a table of values, plot the inverse demand curve.
- Interpret the relationship between price and the quantity demanded.
- Why does the demand curve have a negative slope?
- Find the slope of the demand curve.
- The Total Revenue:
- Create a table of values for the total revenue.
- Graph the total revenue as a function of quantity demanded.
- Describe the relationship between the price and the total revenue.
- The Marginal Revenue:
- Create a table of values for the marginal revenue.
- Graph the marginal revenue function on the same set of axes as the demand curve.
- Describe the relationship between marginal revenue and price.
- Describe the relationship between marginal revenue and the total revenue.
- Find the value of the marginal revenue when the total revenue is a maximum.
- Why is price called average revenue?
- Empirical Functions:
- Find a formula for the inverse demand function.
- Find a formula for the demand function.
- Find a formula for the total revenue function.
- Find a formula for the marginal revenue using the data table.
- Find a formula for the marginal revenue using theoretical principles.
- Elasticity of Demand:
- Define the elasticity of demand
- Create a table of values for elasticity of demand using the point formula.
- Describe the elasticity of demand as price changes.
- Describe the relationship between elasticity of demand and total revenue.
- Describe the relationship between elasticity of demand and marginal revenue.
- Categorize parts of the demand curve based on the elasticity of demand values.
- Monopoly:
- Define a monopoly.
- Assuming that the butter market is a monopoly:
- What portion of the demand curve will the pricing be in? Why?
- What range of values would you expect in marginal revenue?
- What range of elasticities would you expect?