Question

Consider the following production functions: (i) ? = ?? + ??; (ii) ? = 1 2 ? ?? ?; (iii) ? = 2? + 4? ?? ? + 3?? Variables ? and ? are positive parameters. a) Do the above production functions exhibit decreasing, constant, or decreasing returns to scale? Explain how your answer depends on parameters ? and ?. b) Using calculus, derive the marginal product of capital and labor for each of these production functions and then use them to find the MRTS. Under what condition(s) does labor in case (ii) exhibit diminishing marginal returns? Explain. c) For each of the three production functions considered, derive the average product of labor and compare it to the corresponding marginal product of labor.

That is 1/2 for the second function.

Answer 1

we have used concepts:---

1)

f(tK,tL) = t*f(K,L) => constant returns to scale

f(tK,tL) > t*f(K,L) => increasing returns to scale

f(tK,tL) < t*f(K,L) => decreasing returns to scale

2)

APL = f(K,L)/L

3)

MP = first order partial derivative of f(K,L) w.r.t input

4)

MRTS = MPL/MPK