Zuppann, Inc. has just completed a study of its production process for gadgets. It uses labor and capital to produce gadgets. It has determined that 1 more unit of labor would increase output by 200 gadgets. However an additional unit of capital would increase output by 150 gadgets. If the current price of capital is $10 and the current price of labor is $25, is the firm employing the optimal input bundle for its current output? Why or why not? If not, which input’s usage should be increased?

Question

Zuppann, Inc. has just completed a study of its production process for gadgets. It uses labor and capital to produce gadgets. It has determined that 1 more unit of labor would increase output by 200 gadgets. However an additional unit of capital would increase output by 150 gadgets. If the current price of capital is $10 and the current price of labor is $25, is the firm employing the optimal input bundle for its current output? Why or why not? If not, which input’s usage should be increased?

Answer 1

To determine if Zuppann, Inc. is employing the optimal input bundle for its current output, we need to assess the marginal productivity of labor and the marginal productivity of capital in relation to their respective prices.

First, let's calculate the marginal product of labor (MPL) and the marginal product of capital (MPK):

MPL = change in output / change in labor = 200 gadgets per unit of labor
MPK = change in output / change in capital = 150 gadgets per unit of capital

Next, we need to calculate the Marginal Rate of Technical Substitution (MRTS), which measures how many units of capital can be replaced by an additional unit of labor while maintaining the same level of output.

MRTS = MPL / MPK = (200 gadgets / 1 unit of labor) / (150 gadgets / $10 of capital) = (200/1) / (150/$10) = (200/1) * ($10/150) = 20/15 = 4/3

Now, let's compare the MRTS to the price ratio of labor to capital:

Price Ratio = price of labor / price of capital = $25 / $10 = 5/2

If the MRTS is equal to the price ratio, the firm is employing the optimal input bundle. However, if they are not equal, there is an opportunity to increase productivity and decrease cost by reallocating inputs.

In this case, the MRTS (4/3) is not equal to the price ratio (5/2). The MRTS is lower than the price ratio, indicating that the firm is currently employing too much capital relative to labor.

To achieve the optimal input bundle, Zuppann, Inc. should increase the usage of labor and decrease the usage of capital. By doing so, they can increase productivity and reduce costs.