Question

1. A firm is employing 100 hours of labor and 50 tons of cement to produce 500 blocks. Labor costs $4 per hour and cement costs $12 per ton. For the quantities employed,   MP_L = 3 and MP_C = 2. Show this situation in an isoquant-isocost diagram. Is the firm producing at minimum cost? If not, explain and show in the diagram, how the firm can produce the same output at a lower total cost.

Answer 1

The firm is employing 100 hours of labor and 50 tons of cement to produce 500 blocks. This is shown below in the diagram. Wage rental ratio is w/r = 4/12 = 1/3. At the same time MRTS = MPL/MPK = 3/2. Note that at the current combination of (L = 100, K = 50), MRTS > w/r. When this happens it implies that labor is more productive.  This also implies that the firm is not producing at minimum cost. To reduce the cost, firm should increase the use of labor and reduce capital usages so that MRTS declines and reaches the price ratio of 1/3/ This is shown below cost minimizing bundle is (L*, K*).

Сapital Initial condition 50 Long run cost minimization condition К* ISOQUANT (Q 500) 100 L Labor