In this module you learned that cost functions are derived from production functions and that the marginal cost curve is the inverse of the marginal product curve. Work through this problem to demonstrate those findings.

**Production Function:**

Labor (L) | 1 | 3 | 6 | 10 | 15 |

Total Product (Q) | 1 | 2 | 3 | 4 | 5 |

1. Using the production function, compute the figures for marginal product using the definition given earlier in this module. Draw a graph of the marginal product curve using the numbers you computed.

Suppose this firm can hire workers at a wage rate of $10 per hour to work in its factory which has a rental cost of $100. Use the production function to derive the cost function.

2. First compute the variable cost for Q = 0 through Q = 5.

3. Next compute the fixed cost for Q = 0 through Q = 5.

4. Then compute the total cost for Q = 0 through Q = 5. This is the cost function.

5. Finally compute the marginal cost for Q = 0 through Q = 5. Draw the marginal cost curve and compare it to the marginal product curve above. Explain what you see.

## Rubric

Criteria | Not Evident | Developing | Proficient | Distinguished | Weight |

Correctly compute MP for Q = 1 – 5 | 3 | ||||

Correctly draw the marginal cost curve | 1 | ||||

Correctly compute variable cost for Q = 0 – 5 | 3 | ||||

Correctly compute fixed cost for Q = 0 – 5 | 3 | ||||

Correctly compute total cost for Q = 0 – 5 | 3 | ||||

Correctly compute marginal cost for Q = 0 – 5 | 3 | ||||

Draw the graph of marginal cost for Q = 0 – 5. | 1 | ||||

How do the graphs for MC & MP. compare? | 3 | ||||

Total: | __/20 |