4.Suppose the production function for your firm - given units of capital (K) and

Question

4.Suppose the production function for your firm - given units of capital (K) and labor (L) you employ and the current wage rate (w) and rental rate of capital (r) are given as: Q=20 [2L + KL. w=200 r=80 To minimize costs of producing 1000 units of output, you will employ_units of labor and units of capital. Your per-unit cost of production will equal choice in a graph. Illustrate this employment Suppose the rental rate of capital rises to 120. To produce 1000 units you minimize costs employing units of labor and units of capital. Your per-unit cost of production rises to

Explanation / Answer

From the production we know that MRTS = 40/20 = 2. This implies isoquants are straight lines downward sloping. K and L are perfect substitutes

With w/r = 200/80 = 2.5, we see that MRTS < w/r. Hence firm uses only capital as it is cheaper.

To have Q = 1000, we use only capital. 1000 = 20(0L + K)

K* = 50

Note that the isocost line has equation C = wL + rK

C = 200*0 + 80*50

Minimum cost = 4000.

When r = 120, w/r = 200/120 = 5/3 and now MRTS > w/r

This implies firm will now use only labor and 0 units of capital

1000 = 20(2L)

L* = 25 units

Cost now becomes = 25*200 = 5000.

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