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, \(\mathrm{MP}_{t}=5\) apps per month while \(P_{L}=\$ 1,000\) per month. And when it comes to capital, \(\mathrm{MP}_{\mathrm{C}}=8\) apps per month while \(P_{C}=S 1,000\) 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

Decrease labor while increasing capital.

Step-by-step solution

Understand the Problem

To maximize profits, the company should equalize the marginal product per dollar spent on each input. This can be formulated as setting the ratio of marginal product to price equal for labor and capital.

Calculate Marginal Product per Dollar for Labor

The marginal product of labor (MP_L) is 5 apps per month, and the price of labor (P_L) is $1,000 per month. Using the formula: \( \frac{\text{MP}_L}{P_L} = \frac{5}{1000} = 0.005 \) apps per dollar.

Calculate Marginal Product per Dollar for Capital

The marginal product of capital (MP_C) is 8 apps per month, and the price of capital (P_C) is $1,000 per month. Using the formula: \( \frac{\text{MP}_C}{P_C} = \frac{8}{1000} = 0.008 \) apps per dollar.

Compare Marginal Product per Dollar between Labor and Capital

Compare the values calculated in Steps 2 and 3. Since \( 0.008 > 0.005 \), capital is more efficient per dollar spent than labor.

Make the Decision

Since capital provides more apps per dollar spent compared to labor, the company should decrease labor and increase capital to maximize profits.

Key concepts

Marginal Product

The marginal product, often abbreviated as MP, refers to the additional output produced when one more unit of an input is used, keeping other inputs constant. It helps businesses determine how changes in the quantity of input will affect output levels. In our problem, the marginal product of labor (\( \text{MP}_L \)) is given as 5 apps per month, which means that for each extra programmer employed, the company can expect to increase its app production by 5 units. Similarly, the marginal product of capital (\( \text{MP}_C \)), is 8 apps per month, indicating the additional output from using one more computer.
These values are essential to understanding how efficient each input is in producing output and are crucial for making informed business decisions. They guide the firm in assessing which input (labor or capital) is more productive and therefore should be used or increased to enhance production.

Labor and Capital

In economics, labor and capital are the primary factors of production. Labor involves human resources, like the programmers in our scenario, while capital refers to tools and equipment, such as computers. Companies must frequently decide how finely to balance these resources to optimize production.
When considering labor and capital use, it's important to analyze their respective costs and productivity levels. Here, both labor and capital cost $1,000 per month. However, capital is more productive, yielding 8 apps per month compared to labor's production of 5 apps. This discrepancy is a key consideration when strategizing how to allocate resources effectively in order to maximize production and profits.

Profit Maximization

Profit maximization is the ultimate goal for most businesses and entails making decisions that lead to the highest possible profit. In our case, this involves an analysis of the marginal product per dollar spent on each input. The idea is to ensure that every dollar spent is yielding the highest possible output.
To determine this, we calculate the marginal product per dollar for both labor and capital. The results—0.005 apps per dollar for labor and 0.008 apps per dollar for capital—highlight that capital is more efficient in terms of production per dollar spent. Therefore, the company can enhance profits by reallocating resources from less efficient labor to more productive capital, thereby reducing costs and increasing output.

Input Substitution

Input substitution occurs when a company replaces one input with another to increase efficiency or reduce costs. This principle is often applied when seeking to optimize production and use resources more effectively.
In the problem, input substitution is examined through comparing the marginal product per dollar spent on labor and capital. Here, capital shows a higher output per cost, suggesting it's the better investment at the current prices and productivity levels. Therefore, substituting labor with capital becomes a logical strategy for the company to maximize output and, consequently, its profits. This decision reflects a key application of the concept where businesses shift resources to more productive options, achieving broader operational efficiency.