Question

1. A firm faces the following total product curves depending on how much capital it employs. K=1 Unit Quantity of Total Labor Product 100 152 K=2 Units Quantity of Total Labor Product 1 123 1 187 Product WN oloAN K=3 Units Quantity of Total Labor 139 193 263 319 366 407 410 233 249 263 286 306 323 O a. For K=1, calculate the average product and marginal product of labor at each level of labor employed (from labor = 1 to labor = 7). (5%) b. Show the total product curve, average product and marginal product of labor curves graphically (from labor = 1 to labor = 7). (5%) C. Suppose that the firm currently employs 1 unit of capital and 3 of labor. Compute MRTS. Compute MPL Compute MPK. (10%) d. Suppose that the amount of capital would be fixed at 2 units. The price of capital is $4 per unit and the price of labor is $10 per unit. What is the short-run total cost of producing 263 units of output? (5%) What is the long-run total cost of producing 263 units of output? (10%) e. Suppose that the price of capital increases to $20 per unit and the price of labor falls to $5 per unit. Now what is the long-run total cost of producing 263 units of output? (10%) f. Beginning with 1 unit of capital and 2 units of labor, does this production function exhibit increasing, constant, or decreasing returns to scale? Explain your answer. (10%)

Answer 1

Average product of labor is given by the following formula:

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Marginal product of labor is the increment in the total revenue from the addition of one more unit of labor.

Average product of labor is given by the following formula:

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a.

For K=1, calculate the average product and total product of labor as follows:

Quantity of labor	Total Product	Average Product	Marginal Product
1	100	100/1 = 100	-
2	152	152/2 = 76	152 –100 = 52
3	193	193/3 = 64.33	193 –152 = 41
4	215	215/4 = 53.75	215 –193 = 22
5	233	233/5 = 46.6	233 –215 = 18
6	249	249/6 = 41.5	249 –233 = 16
7	263	263/7 = 37.57	263 –249 = 14

b.

Show the TP, MP, and AP curves as follows:

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c.

The following is the formula for MRTS:

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When K is constant at 1, the MP_L is 215-193 = 22 and MP_K is 263-215 = 48

Therefore, MRTS is 22/48 = 0.4583

d.

When the firm employs 2 units of capital and produces 263 units of output, it will need 4 units of labor.

Calculate the short run total cost as follows:

Therefore, SRTC is $48

Check the output level of 263 in all the 3 instances of K being 1,2, and 3.

Calculate the long run total cost as follows:

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As TC are minimized at L=3 and K=3. Therefore, LRTC is $42