Assuming that the person reading this has very little or no previous economic knowledge, I have to address the following:
For each producton function determine the marginal rate of technical substitution of labour for capital and answer "yes" or "no" for each whether the production function will have a diminishing marginal productivity of labour, of capital, and of marginal rate of technical substitution. Please explain the answers or reasoning to each "yes" or "no" answer for diminishing MPL, MPK, and MRTS.
1. If Q=L+K, and MPL=1 and MPK=1.... what is MRTS equal to? Is MPL diminishing? Is MPK diminishing? Is MRTS diminishing?
2. If Q= (LK)^0.5, and MPL=0.5(K/L)^0.5 and MPK=0.5(L/K)^0.5 .... what is MRTS equal to? Is MPL diminishing? Is MPK diminishing? Is MRTS diminishing?
3. If Q=(L^3)(K^3), and MPL=3L^2(K^3) and MPK=3L^3(K^2) .... what is MRTS equal to? Is MPL diminishing? Is MPK diminishing? Is MRTS diminishing?
4. If Q=L^2 + K^2, and MPL=2L and MPK=2K .... what is MRTS equal to? Is MPL diminishing? Is MPK diminishing? Is MRTS diminishing