If the production function is $q=f(L, K)=3 L+$ $2 K,$ and capital is fixed at $\bar{K}=50,$ what is the short-run production function? What is the marginal product of labor? (Hint: See Solved Problem 6.1.)
Added by Salvador D.
Step 1
Step 1: Given the production function $q=f(L, K)=3L+2K$ and capital is fixed at $\bar{K}=50$, we can substitute $\bar{K}=50$ into the production function to get the short-run production function: $q=3L+2(50)$ $q=3L+100$ Show more…
Show all steps
Your feedback will help us improve your experience
Banhishikha Sinha and 61 other Microeconomics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The equation below is a production function: Q = (200)L + (100)K - (0.2)L^2 - (0.1)K^2, where Q is output, L is labor, and K is capital. What is the Marginal Product of Labor of this function?
Andrew D.
Suppose that the production function is $q=L^{0.56} K^{0.48}$ a. What is the average product of labor, holding capital fixed at $\bar{K}$ ? $\mathbf{A}$ b. What is the marginal product of labor? (Hints: See Solved Problem $6.1 .$ Calculate how much $q$ changes as $L$ increases by 1 unit for a particular pair of $K$ and $L,$ use calculus, or see Appendix $6 \mathrm{C}$.) $\mathrm{C}$
Firms and Production
Short-Run Production
Marginal Product of Labor The output y of a manufacturing process is a function of the size of the labor force n using the function $y=k \sqrt{n}$ The marginal product of labor, defined as $d y / d n,$ measures the rate that output increases with the size of the labor force, and is a measure of labor productivity.(a) Show that $\frac{d y}{d n}=\frac{k}{2 \sqrt{n}}$ (b) How can you tell from your answer to part (a) that as the size of the labor force increases, the marginal product of labor gets smaller? This is a phenomenon known as the law of diminishing returns, discussed more in the next chapter.
Calculating the Derivative
Techniques for Finding Derivatives
Recommended Textbooks
Principles of Economics
Principles of Microeconomics for AP® Courses
Economics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD