1.
Producer Theory Practice Set 1
V. Bardis
(Note: The following are (some of the) synonyms for "Marginal Rate of Technical Substitution": MRS, TRS , MRTS, RTS.)
For each of the following production functions, derive and interpret the degree of homogeneity.
q =
q =
q =
q =
2. The following is a simplified version of the production function known as the "C.E.S. function" in economics (fo
Constant Elasticity of Substitution). Show that the C.E.S. function exhibits constant returns to scale for all r.
3. Show that the following functions are not homogeneous.
4.
5.
q
q
(given L>1 and K>2; F(L,K) = 0, otherwise)
6. On the same graph, plot the isoquant for q=1 for the following two production functions:
noting that the two curves intersect at the point where L=1 and K=1.
a) How do their MRS's differ at the point where they intersect?
) Identify a point on each curve such that the MRS is the same. How do they differ at the points where thei
MRS has the same value?
7. On the same graph, plot the isoquant for q=1 for the following three production functions: the function in
question 4, production function q = G(L,K) = min(L,K) and the production function q = H(L,K) =(L+K)/2.
How do they differ at the point where they intersect.
8. Find the marginal rate of substitution (=-dK/dL) for the following production function and
show that it decreases as L increases. Are the isoquants of the production function concave o
convex curves?
9. For each production function below, find the marginal product of each input and determine how each input's
marginal product changes if (i) more of this input is used holding the other input constant and (ii) more of the other
input is used holding this input constant.
(given L>1 and K>2; H(L,K) = 0, otherwise)
10. Consider the function F(L,K) = 4L +2K + 4. Is this a valid production function? Explain.