According to production engineers, the firm’s production function gives the following outputs that can be produced from various combinations of labor and capital. The firm can purchase labor services (w) for $20 per unit and capital services (r) for $40 per unit.

a. If the firm wishes to produce 87 units of output, which input combination is technically efficient: 5L and 1K, 4L and 2K, 3L and 3K, or 2L and 4K? Explain your answer.

b. If the firm wishes to produce 87 units of output, which input combination is economically efficient: 5L and 1K, 4L and 2K, 3L and 3K, or 2L and 4K? Explain your answer.

c. If input prices change to $40 per unit of labor (w = 40) and $20 per unit of capital (r = $20), what is the economically efficient input combination to produce 87 units? Explain.

d. Suppose the firm operates in the short run with 3 units of capital. Does the marginal productivity of labor increase or decrease when the units of labor increase? Explain using the production data in the preceding table

e. Suppose the firm was operating initially at a scale of production implying the use of 2 units of labor and 2 units of capital. What is the production obtained? Supposed then that the scale of production is 6 / 6 doubled, namely the firm produces now with 4 units of labor and 4 units of capital. What is the production level now? Does the firm present economies or diseconomies of scale? Why?

Units of Capital 2 22 20 28 40 87 137 197 2 42 62 77 45 69 87 58 87 Units of Labor 110 2.