Please provide the explanation on the approach to the solution.1
Problem Set 2
Due on Tuesday February 16th at the beginning of class
Please write on your homework your full name, as it appears in Blackboard, and your
student ID number.
Write neatly and show how you arrived at every single answer on the
You will receive ZERO credit for any answer where you don’t show your
(5pts) Identify the returns to scale of the following production functions:
°(?, ?) = ?
°(?, ?) = 2?
°(?, ?) = ?
°(?, ?) =
(5pts) From the production functions above, select the one that exhibits Constant
Returns to Scale (CRTS) and compute the marginal product of labor, marginal
product of capital, average product of labor, and average product of capital. Does
the law of diminishing marginal returns hold? Why?
(5pts) Derive the Marginal Rate of Technical Substitutions (MRTS) between
capital and labor for the production function selected above. Does the law of
diminishing MRTS hold? Why? Derive the equation for a sample isoquant and
draw three isoquants for the production function selected above. Be sure to label
as many points as you can.
(5pts) Compute and interpret the elasticity of substitution at point (K
) = (2,2)
when capital is increased by one unit.
(30 pts) Consider a firm that uses two inputs, capital (K) and labor (L), to produce
output (Q). The production function is given by:
Q = L
. The firm can hire as much labor as it wants at a wage of w=$
hour and can rent as much capital as it wants at a price of r=
(5 pts) Does the production function exhibit constant, decreasing, or
increasing returns to scale?
(5 pts) Solve for the optimal input combination to produce 100 units of output.
(5 pts) For arbitrary values of w, r, and Q, solve for the (long run) input
(5 pts) For arbitrary values of w, r, and Q, solve for the long run cost function.
Graph this cost function when w=$
Derive the long run average cost function. Does this cost function
exhibit economies of scale, diseconomies of scale, or constant returns to
(5 pts) Suppose that the firm's capital is fixed in the short run at
firm's short run demand for labor and the corresponding cost function.