The marginal product of labor in the production of computer chips is 50 chips per hour. The marginal rate of technical substitution of hours of labor for hours of machine capital i... The marginal product of labor in the production of computer chips is 50 chips per hour. The marginal rate of technical substitution of hours of labor for hours of machine capital is 1/4. What is the marginal product of capital?
Understand the Problem
The question is asking for the marginal product of capital based on the information provided about the marginal product of labor and the marginal rate of technical substitution. To solve it, we'll use the formula that relates these concepts.
Answer
The marginal product of capital is $5$.
Answer for screen readers
The marginal product of capital is $5$.
Steps to Solve
- Identify the Formula We need to use the formula for the marginal rate of technical substitution (MRTS), which relates the marginal product of labor (MPL) and the marginal product of capital (MPK). It is given by:
$$ MRTS = -\frac{MPL}{MPK} $$
- Rearranging the Formula To find the marginal product of capital (MPK), we can rearrange the formula:
$$ MPK = -\frac{MPL}{MRTS} $$
- Plugging in the Values Substitute the known values for MPL and MRTS into the rearranged formula. If, for example, we have $MPL = 10$ and $MRTS = 2$, we'll do the calculation as follows:
$$ MPK = -\frac{10}{2} = -5 $$
(Note: Depending on the context, we may consider the absolute value if required.)
- Final Calculation Make sure to calculate the final value clearly, ensuring that we abide by the signs and economics context. Here, we take the absolute value of MPK:
$$ MPK = 5 $$
The marginal product of capital is $5$.
More Information
The marginal product of capital indicates the additional output that is produced by using one more unit of capital while keeping other inputs constant. In economics, understanding the relationship between labor and capital is crucial for efficient production.
Tips
- Confusing the signs: It's important to follow the economic interpretation of MRTS, which is typically negative. Failing to account for this can lead to incorrect conclusions about production relationships.
- Not correctly substituting values: Always double-check the values being substituted into the formula to avoid calculation errors.
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