Economics Prof. Andrew
A. Swash Buckles
Enterprises produces swash buckles (Q) using only labor (L). Let AP(L)
and MP(L) represent EF's average and marginal products of labor at quantity
L. Fill in the blanks in the following
production function for apples on the Eris Island is Q = 8L1/2T1/2,
where Q is the quantity of apples produced, L is the quantity of labor, and
T is the quantity of land. This is an example of a Cobb-Douglas production
function. (See Appendix or the WWW for a brief review of exponents.)
B.1. In 1982,
farmers on Eris devoted 900 square miles to apple production. Write
the equation for
the average product of labor as a function of L in that year.
B.2. The associated
marginal product of labor function when T=900 is MP(L) = 120L-1/2.
taking the first derivative of the production function with respect to L at
T = 900.)
When L = 64 what is the marginal product of labor?
below are five production functions showing output (Q) as a function of
labor (L) and capital (K). In each case, determine whether the production
process exhibits increasing (I), decreasing (D), or constant (C) (maginal)
returns to scale and then whether it exhibits increasing (I),
decreasing (D), or constant (C) returns to labor. Indicate your
choices under the appropriate columns. Remember that returns to scale
calculations require that both factors change by the same proportion, while
returns to labor calculations require that L change with K held constant.
The first one is done for you.
Hostess, Ltd. produces manna (low-fat and regular) for sale over the
internet using two ingredients, milk and honey. The entries in the table
show how the company's daily output (measured in tons) varies with the
quantities of the inputs.
D1. Does manna
production exhibit Increasing,
Does manna production exhibit Increasing,