Question

Suppose a firm with a production function Q = KL (where MPL = K and MPK = L) is producing 125 units of output by using 5 workers and 25 units of capital. The wage rate (W) per worker is $10 and the rental per unit of capital (R) is $2. What is the firm’s long-run average total cost, and what will it be if output falls to 45 units?

Answer 1

The answer is "rises from $0.80; $1.33".

Step-by-step explanation:

please find the complete question in the attached file.

Production companies use, as per the estimates, 5 employees and 25 capital units. Its pay rate is 10 $per employee as well as the rate is 2 $per employee. Thus the overall cost of the production of 125 units.

`\to TC = PL * L + PK * K \\\\`

`= 10* 5 + 2 * 25 \\\\= 50 + 50 \\\\ = \$ \ 100 \\`

`ATC = (TC)/(Q)`

`= (100)/(125)\\\\= \$ \ 0.80`

The production has been reduced to 45 unit efficiency, however, the cost is similar. We also measure for optimum labor, thus, ATC also will decrease

`\to (MPL)/(MPK) = (PL)/(PK) \\\\\to (K)/(L) = (10)/(2) \\\\\to K = 5\ L`

Place it in the production process,

`\to Q = KL\\\\\to 45 = (5L) L\\\\\to 45 = 5 L^2`

when L = 3 and K = 15:

`\to TC = 3* 10 + 15 * 2\\\\`

`= 30 + 30\\\\= 60`

`\to ATC = (TC)/(Q)\\\\`

`= (60)/(45)\\\\= \$ \ 1.33`