Question

A software company in Silicon Valley uses programmers (labor) and computers (capital) to produce apps for mobile devices. The firm estimates that when it comes to labor, \(\mathrm{MP}_{L}=\) 5 apps per month while \(P_{L}=\$ 1,000\) per month. And when it comes to capital, \(\mathrm{MP}_{C}=8\) apps per month while \(P_{C}=\$ 1,000\) per month. If the company wants to maximize its profits, it should: a. Increase labor while decreasing capital. b. Decrease labor while increasing capital. c. Keep the current amounts of capital and labor just as they are. d. None of the above.

Short answer

b. Decrease labor while increasing capital.

Step-by-step solution

Understanding Marginal Product

We begin with the concept of Marginal Product (MP), which measures the additional output produced by an additional unit of input. Here, \(\mathrm{MP}_L = 5\) apps means that one additional programmer generates 5 more apps per month. Likewise, \(\mathrm{MP}_C = 8\) apps indicates that one more computer generates 8 more apps per month.

Analyzing Costs and Benefits

Next, consider the costs: the price of each additional unit of labor (programmer) is \(P_L = \\(1000\), and the price for each additional unit of capital (computer) is \(P_C = \\)1000\). The firm should aim to equalize the marginal benefit per dollar spent on each input to maximize profits.

Calculate Marginal Product Per Dollar

For labor, the marginal product per dollar is \(\frac{\mathrm{MP}_L}{P_L} = \frac{5}{1000} = 0.005\). For capital, it's \(\frac{\mathrm{MP}_C}{P_C} = \frac{8}{1000} = 0.008\). The marginal product per dollar is higher for capital than for labor.

Determine Optimal Input Mix

Since the marginal product per dollar for capital (0.008) is greater than for labor (0.005), the company should invest more in capital and less in labor to maximize its profits. Hence, the optimal strategy is to decrease labor and increase capital.

Key concepts

Marginal Product

The marginal product is an economic concept that helps us understand the contribution of each additional unit of input to the total output. In simpler terms, it's like asking, "What do we get if we add one more programmer or one more computer to the mix?"

In the given problem, we are looking at two types of inputs: labor (programmers) and capital (computers). The marginal products given are

1. \( \mathrm{MP}_L = 5 \): Each additional programmer produces 5 more apps per month.
2. \( \mathrm{MP}_C = 8 \): Each additional computer produces 8 more apps per month.

Understanding these numbers helps companies make decisions about resource allocation. If we see that one resource creates a more significant uptick in production compared to another, it might be worth looking into how we can effectively utilize or increase its presence in our production process.

Input Optimization

In the context of business operations, input optimization is about making the most out of your available resources in order to achieve the desired goals. How do you decide whether to hire more labor or invest in more capital? This decision often revolves around balancing costs and benefits.

In our scenario, we have the cost of hiring a programmer as \( P_L = \\(1000 \) and the cost of acquiring an additional computer as \( P_C = \\)1000 \). To find the best mix of inputs, a company should consider the marginal product per dollar spent on each input. This helps to understand which input gives more bang for the buck.

• For labor, the calculation is \( \frac{\mathrm{MP}_L}{P_L} = \frac{5}{1000} = 0.005 \).
• For capital, it's \( \frac{\mathrm{MP}_C}{P_C} = \frac{8}{1000} = 0.008 \).

Assessing these values tells the company which resource is providing a greater return on investment, guiding whether to allocate more funds toward labor or capital.

Cost-Benefit Analysis

Cost-benefit analysis is a fundamental method used to determine whether a particular business decision is worthwhile. In simple terms, it's about comparing what you gain with what you spend. In the case at hand, the company evaluates whether adding more programmers or more computers is a better decision, financially speaking.

With both the cost and output potential quantified, companies can decide where to put their money for the maximum output. Since the marginal product per dollar is higher for capital (0.008) than for labor (0.005), this explains why the company should reduce spending on labor and invest more in capital.

This systematic approach helps in ensuring that the investments made by the company are always oriented towards maximizing profitability and efficiency. It's like choosing the path that leads to the best value for money, contributing significantly to economic efficiency.