Consider the production function Q = f(L,K) = 10KL / K+L. The
marginal products of labor...
Consider the production function Q = f(L,K) = 10KL / K+L. The
marginal products of labor and capital for this function are given
by
MPL = 10K^2 / (K +L)^2, MPK = 10L^2 / (K +L)^2.
(a) In the short run, assume that capital is fixed at K = 4.
What is the production function for the firm (quantity as a
function of labor only)? What are the average and marginal products
of labor? Draw APL and MPL on one...
2. Consider the following production functions, to be used in
this week’s assignment:
(A) F(L, K)...
2. Consider the following production functions, to be used in
this week’s assignment:
(A) F(L, K) = 20L^2 + 20K^2
(B) F(L, K) = [L^1/2 + K^1/2]^2
a (i) Neatly draw the Q = 2,000 isoquant for a firm with
production function (A) given above, putting L on the horizontal
axis and K on the vertical axis. As part of your answer, calculate
three input bundles on this isoquant. (ii) Neatly draw the Q = 10
isoquant for a firm...
The production function at Jerry’s Copy Shop is q=1000min(L,3K)
, where q is the number of...
The production function at Jerry’s Copy Shop is q=1000min(L,3K)
, where q is the number of copies per hour, L is
the number of workers, and K is the number of copy
machines. Draw the following graphs. The graphs should have the
number of workers, L, on the x-axis.
Draw the isoquants for this production function for q =
1000, 2000, and 3000. [4 pts.]
Draw the total product of labor (TPL), average
product of labor (APL), and marginal product...
Draw isoquant curve for the following production functions.
Here ?Kdenotes quantity of capital input and ?Ldenotes...
Draw isoquant curve for the following production functions.
Here ?Kdenotes quantity of capital input and ?Ldenotes the
quantity of labor input.
In the graph, let ?Kbe on the vertical axis and ?Lbe on the
horizontal axis.
(a) ?(?,?)=?⋅?=?¯,F(K,L)=K⋅L=Q¯,where
(1) ?¯=100,Q¯=100,
(2) ?¯=200,Q¯=200,
(3) ?¯=300.Q¯=300.
This production function is an example of Cobb-Douglas
production technology.
(b) ?(?,?)=2?+5?=?¯,F(K,L)=2K+5L=Q¯,where
(1) ?¯=100,Q¯=100,
(2) ?¯=200,Q¯=200,
(3) ?¯=300.Q¯=300.
This production function is an example of perfect substitutes
production technology.
(c) ?(?,?)=min{2?,5?}=?¯,F(K,L)=min{2K,5L}=Q¯,where
(1) ?¯=100,Q¯=100,
(2) ?¯=200,Q¯=200,
(3)...
Draw isoquant curve for the following production functions.
Here ?Kdenotes quantity of capital input and ?Ldenotes...
Draw isoquant curve for the following production functions.
Here ?Kdenotes quantity of capital input and ?Ldenotes the
quantity of labor input.
In the graph, let ?Kbe on the vertical axis and ?Lbe on the
horizontal axis.
(a) ?(?,?)=?⋅?=?¯,F(K,L)=K⋅L=Q¯,where
(1) ?¯=100,Q¯=100,
(2) ?¯=200,Q¯=200,
(3) ?¯=300.Q¯=300.
This production function is an example of Cobb-Douglas
production technology.
(b) ?(?,?)=2?+5?=?¯,F(K,L)=2K+5L=Q¯,where
(1) ?¯=100,Q¯=100,
(2) ?¯=200,Q¯=200,
(3) ?¯=300.Q¯=300.
This production function is an example of perfect substitutes
production technology.
(c) ?(?,?)=min{2?,5?}=?¯,F(K,L)=min{2K,5L}=Q¯,where
(1) ?¯=100,Q¯=100,
(2) ?¯=200,Q¯=200,
(3)...
1. Consider the following production function:
Y=F(A,L,K)=A(K^α)(L^(1-α))
where α < 1.
a. Derive the Marginal Product...
1. Consider the following production function:
Y=F(A,L,K)=A(K^α)(L^(1-α))
where α < 1.
a. Derive the Marginal Product of Labor(MPL).
b. Show that this production function
exhibit diminishing MPL.
c. Derive the Marginal Production of Technology (MPA).
d. Does this production function exhibit diminishing MPA? Prove
or disprove
Bonus Question. Suppose the production function for a firrm is
Q(K,L) = K1/2L1/2, so the marginal...
Bonus Question. Suppose the production function for a firrm is
Q(K,L) = K1/2L1/2, so the marginal product of labor is MPL = 1 2
K1/2L−1/2 and the marginal product of capital is MPK = 1 2
K−1/2L1/2.
a) Find the equation of the isoquant for Q = 1. That is, when Q
= 1, find L as a function of K or K as a function of L to obtain an
equation for the isoquant.
b) Find K1, K2, L3,...
A firm has the production function:
Q = L 1 2 K 1 2
Find the...
A firm has the production function:
Q = L 1 2 K 1 2
Find the marginal product of labor (MPL), marginal
product of capital (MPK), and marginal rate of technical
substitution (MRTS).
Note: Finding the MRTS is analogous to finding the
MRS from a utility function:
MRTS=-MPL/MPK. Be sure to simplify your
answer as we did with MRS.
A firm has the production function:
Q = L 1 2 K 3 4
Find the marginal product of labor (MPL),...
Given the short run production function, Q = 3L2 –
0.1L3
( a) Write down the...
Given the short run production function, Q = 3L2 –
0.1L3
( a) Write down the equations for,
(i) the marginal product of labor, MPL
(ii) the average product of labor, APL.
(b) Find the value of Q for which the MPL and APL are
maximized.
(c) Show that the MPL= APL when the APL is at a maximum