# Chapter 1. Figure It Out 7.4

## 1.1Screen 1 of 3

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Steve and Sons Solar Panels has a production function represented by Q = 4KL, where the MPL = 4K and the MPK = 4L. The current wage rate (W) is \$8 per hour, and the rental rate on capital (R) is \$10 per hour.

In the short run, the plant’s capital stock is fixed at K = 10. What is the cost the firm faces if it wants to produce Q = 200 solar panels?

### Question

The firm’s total cost will be \$ CnS5fpClBb1CZQjf

The production function shows that in order to produce 200 solar panels using 10 units of capital, the firm will need to hire 5 units of labor. So, the firm will pay 10 units of capital \$10 each, and 5 units of labor \$8 each, for a total of \$140. For further review, see section “Short-Run and Long-Run Cost Curves”.

## 1.2Screen 2 of 3

### Question

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## 1.3Screen 3 of 3

What will the firm’s cost of producing 200 solar panels be if Steve and Sons minimizes costs in the long run?

### Question

Steve and Sons’ minimum long-run cost of producing 200 solar panels is \$ DyhjcncZ/3zWxZD98hC3EQ5WaiW4Rj6qyn203dkuGFKrAintxqANqRxnF+TXmt3w (round answer to two decimal places).

When Steve and Sons minimizes costs, MPL/MPK = W/R. For this problem, MPL/MPK = K/L; W/R = 0.8. So, when Steve and Sons minimizes costs, K/L = 0.8, or K = 0.8L; Steve should hire 4 units of capital for every 5 units of labor. Steve’s production function is Q = 4KL. We know that Q = 200, and that K = 0.8L. Substituting, 200 = 4(0.8L)(L). Solve to find L = 7.91; K = 0.8(7.91) or 6.33. Steve and Sons will spend \$8(7.91) or \$63.28 on labor; Steve and Sons will spend \$10(6.33) or \$63.30 on capital, for a total cost of \$126.58. For further review, see section “Short-Run and Long-Run Cost Curves”.