Amy's Performance Pizza is a small restaurant in San Francisco that sells gluten-free pizzas. Amy's very tiny kitchen has barely enough room for the three ovens in which her workers bake the pizzas. Amy signed a lease obligating her to pay the rent for the three ovens for the next year. Because of this, and because Amy's kitchen cannot fit more than three ovens, Amy cannot change the number of ovens she uses in her production of pizzas in the short run. a. However, Rosa's decision regarding how many workers to use can vary from week to week because her workers tend to be students. Each Monday, Rosa let them know how many workers she needs for each day of the week. In the short run, these workers are (fill in the blank) inputs, and the ovens are (fill in the blank) inputs.

Rosa's daily production schedule is presented in the following table:

Number of Workers Output (Pizzas) Marginal Product of Labor (Pizzas)
0 0 -
1 60
2 100
3 130
4 150
5 160

b. Fill in the blanks to complete the Marginal Product of Labor column for each worker.
c. On the following graph, plot Rosa's production function using a green line.
d. Supposed that labor is Rosa's only variable input cost and that she has a fixed cost of $20 per day and pay each of her workers $30 per day. Use an orange line to plot Rosa's total cost curve on the following graph using the quantities from the preceding table.
e. True or False: The shape of the production function reflects the law of increasing marginal returns.

Solution :

Amy can only change the number of workers. As the fixed input cannot be changed in the short run, so in the short run, the workers are the variable inputs and the ovens are the fixed inputs.

a). Marginal Product of labor

  No. of workers    The Output    The Marginal product of labor

   0                           0                           ---

   1                            60                        60

   2                           100                       40

   3                           130                       30

   4                           150                       20

   5                           160                       10

The marginal product of the labor is the change in the quantity i.e pizza as Amy hires an additional worker.

1 worker raise the output to 100, so the marginal product of labor of 1 worker is 100 and so on. The marginal product of the labor = change in the output / change in the number of workers.

b).

No. of workers   The Output    The Fixed cost  The Variable cost Total cost

       0                            0              20                        0                          20

       1                            60             20                       30                         50

      2                            100             20                      60                       80

      3                            130             20                       90                       110

      4                            150            20                        120                      140

     5                             160            20                        150                      170

The fixed cost remains the same but the variable cost increases as one more worker is hired.

The law of the diminishing the marginal product of labor is determined by = total output increases at the decreasing rate as we increase the quantity of the labor.      

d. all of the above are true.