Chapter . Section 13, Problem 3
Step 1
Work It Out
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You must read each slide, and complete any questions on the slide, in sequence.
Question
Patty’s Pizza Parlor has the production function per hour shown in the accompanying table. The hourly wage rate for each worker is $10. Each pizza sells for $2.
| Quantity of labor (workers) | Quantity of pizza |
|---|---|
| 0 | 0 |
| 1 | 9 |
| 2 | 15 |
| 3 | 19 |
| 4 | 22 |
| 5 | 24 |
Calculate the marginal product of labor for each worker and the value of the marginal product of labor per worker.
| Quantity of labor (workers) | Quantity of pizza | MPL (pizzas per worker) | VMPL1 (per worker) (price of pizza = $2) |
|---|---|---|---|
| 0 | 0 | ||
| 1 | 9 | Q3PdQ4iKdKE= | $XfbQwBcbq1Q= |
| 2 | 15 | yBhAQ+3VvjM= | DDH6Tw1RFEk= |
| 3 | 19 | h4XZagboIgc= | L6bSXEGJIC8= |
| 4 | 22 | 607M7xmPORU= | yBhAQ+3VvjM= |
| 5 | 24 | XvVM00l89Is= | h4XZagboIgc= |
The marginal product of labor is calculated as the change in the quantity of pizza’s made divided by the change in the quantity of labor. As Patty hires one worker, the quantity of pizza’s made increases from zero to 9. Thus, the marginal product of the first worker is 9 pizzas. The value of the marginal product of labor per worker is found by multiplying the marginal product of labor by the price of each pizza. The first worker can produce 9 pizzas which sell for $2 per pizza giving a value of $18 to the first workers output. For further review see section, “Value of the Marginal Product.”
Calculate the marginal product of labor for each worker and the value of the marginal product of labor per worker.
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Step 2
Question
Patty’s Pizza Parlor has the production function per hour shown in the accompanying table. The hourly wage rate for each worker is $10. Each pizza sells for $2.
| Quantity of labor (workers) | Quantity of pizza | MPL (pizzas per worker) | VMPL1 (per worker) (price of pizza = $2) |
|---|---|---|---|
| 0 | 0 | ||
| 1 | 9 | 9 | $18 |
| 2 | 15 | 6 | 12 |
| 3 | 19 | 4 | 8 |
| 4 | 22 | 3 | 6 |
| 5 | 24 | 2 | 4 |
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Step 3
Question
Now the price of pizza increases to $4. Calculate the value of the marginal product of labor per worker, how many workers Patty should employ now.
| Quantity of labor (workers) | Quantity of pizza | MPL (pizzas per worker) | VMPL1 (per worker) (price of pizza = $4) |
|---|---|---|---|
| 0 | 0 | ||
| 1 | 9 | 9 | $SBORzTQMUMc= |
| 2 | 15 | 6 | 7dfNq0tWt7c= |
| 3 | 19 | 4 | zhw5AiG32jY= |
| 4 | 22 | 3 | DDH6Tw1RFEk= |
| 5 | 24 | 2 | L6bSXEGJIC8= |
How many workers should Patty hire? h4XZagboIgc=
The MPL is calculated by taking the change in the quantity of pizzas divided by the change in the quantity of labor. The VMPL is calculated by multiplying the MPL by the price of pizza, which is now $4.The new value of the marginal product of labor equals the wage rate at 4 workers. So Patty should employ 4 workers. For further review see section, “Value of the Marginal Product and Factor Demand.”
Now the price of pizza increases to $4. Calculate the value of the marginal product of labor per worker, how many workers Patty should employ now.
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Step 4
Question
Now let’s assume that Patty buys a new high-tech pizza oven that allows her workers to become twice as productive as before. That is, the first worker now produces 18 pizzas per hour instead of 9, and so on.
Calculate the new marginal product of labor and the new value of the marginal product of labor.
| Quantity of labor (workers) | Quantity of pizza | MPL (pizzas per worker) | VMPL1 (per worker) (price of pizza = $2) |
|---|---|---|---|
| 0 | 0 | ||
| 1 | 18 | XfbQwBcbq1Q= | $SBORzTQMUMc= |
| 2 | 30 | DDH6Tw1RFEk= | 7dfNq0tWt7c= |
| 3 | 38 | L6bSXEGJIC8= | zhw5AiG32jY= |
| 4 | 44 | yBhAQ+3VvjM= | DDH6Tw1RFEk= |
| 5 | 48 | h4XZagboIgc= | L6bSXEGJIC8= |
The MPL is calculated by taking the change in the quantity of pizzas divided by the change in the quantity of labor. You will notice the MPL has doubled. The VMPL is calculated by multiplying the MPL by the price of pizza, which is $2.The new value of the marginal product of labor equals the wage rate at 4 workers. So Patty should employ 4 workers. For further review see section, “Value of the Marginal Product and Factor Demand.”
Calculate the new marginal product of labor and the new value of the marginal product of labor.
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Step 5
Question
Now let’s assume that Patty buys a new high-tech pizza oven that allows her workers to become twice as productive as before. That is, the first worker now produces 18 pizzas per hour instead of 9, and so on.
qJtAhc0j5uwr7YqZ1HWr/Fair2NFbLZG+/LPRV5Wi6qFbDfNI5ep9NldjDSlBaZptiHkMyNv8vOf/oPli36Ny4gwRyW+EN5eCz3BmmjQuVqNARVV3tfxRvSfmQfqBHPZOuVstnyXoA/7ScVNeCnche5s3WAAtTAvcEeDa4wO9RRjWbOXFZzPOq1PgV77TAHUOPWMkNBJHVZfX23rThe value of the marginal product of labor now equals the wage rate at 4 workers. So Patty should employ 4 workers. As the value of the marginal product of labor increases—in this case as a result of a technological innovation (the new pizza oven)—Patty should hire more workers. For further review see section, “Value of the Marginal Product and Factor Demand.”
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