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Chapter 7: Problem 16

Suppose that a paving company produces paved parking spaces \((q)\) using a fixed quantity of land \((T)\) and variable quantities of cement (C) and labor (L). The firm is currently paving 1000 parking spaces. The firm's cost of cement is \(\$ 4,000\) per acre covered, and its cost of labor is \(\$ 12 /\) hour. For the quantities of \(C\) and \(L\) that the firm has chosen, \(M P_{C}=50\) and \(M P_{L}=4\) a. Is this firm minimizing its cost of producing parking spaces? How do you know? b. If the firm is not cost-minimizing, how must it alter its choices of \(C\) and \(L\) in order to decrease cost?

Short Answer

Expert verified
Given the unequal ratios of the marginal products to the prices of the inputs, the firm is not minimizing costs. The firm should decrease its usage of cement and increase its usage of labor to minimize costs. This process should continue until the additional output obtained per dollar spent on each input is equal.

Step by step solution

01

Calculate the Marginal Product per Dollar for Each Factor

First, calculate the ratios of the marginal products to the cost of each factor of production. For cement, this is \(MP_C/P_C = 50/4000 = 0.0125\) paved spaces per dollar. For labor, this is \(MP_L/P_L = 4/12 = 0.333\) paved spaces per dollar.
02

Compare the Marginal Product per Dollar

Compare these ratios. In this case, \(MP_C/P_C < MP_L/P_L\). The marginal product per dollar spent on labor (0.333) is higher than the marginal product per dollar spent on cement (0.0125).
03

Conclude Whether the Firm is Minimizing Costs

Given that \(MP_C/P_C\) is not equal to \(MP_L/P_L\), the firm is not minimizing costs.
04

Provide Solution for Cost Reduction

If the firm needs to decrease its costs, it should alter its choice of inputs. The firm should switch its spending away from cement (which provides 0.0125 spaces per dollar) towards labor (which provides 0.333 spaces per dollar), until the ratios are equal.

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