Chapter 1. Figure It Out 7.4
1.1 Screen 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”.
1.2 Screen 2 of 3
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1.3 Screen 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”.