Question

Suppose the production function for a bakery is: Q = 4K0.4L0.6 where Q is the number of loaves of bread produced per day, K is the number of ovens, and L is the number of workers employed. Use calculus for the following:

a. determine a function for the marginal product of labor.

b. determine a function for the marginal product of capital.

c. find the marginal rate of technical substitution.

d. discuss how MRTSLK changes as the firm uses more labor, holding output constant.

Answer #1

4. output Q according to the production function
Q = 6K1/3L1/2, where K = capital and L
=labor.
A. Calculate the marginal product of capital.
Calculate the marginal product of labor.
Calculate the marginal rate of technical substitution
A technological advance occurs which changes the production
function to Q = 2KL.
D. Calculate the new marginal product of capital.
E. Calculate the new marginal product of labor.
F. Calculate the new marginal rate of technical substitution for
Lazy J Enterprises....

For each of the following production functions: a)
Q(K,L) = 2K + 3L b) Q(K,L) = K^0.5L^0.25 c)Q(K,L) = LK +
L
Write an equation and graph the isoquant for Q =
100. ?
Find the marginal rate of technical substitution and
discuss how M RT SLK ?changes as the firm uses
more L, holding output constant. ?

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...

Suppose, the production function for X company is given by ? =
5(??) 0.5 where, Q is the amount of output produced, K is the
amount of capital employed in production and L is the amount of
labor employed in production. The prices of capital and labor are
given by ?? = $48 and ?? = $75.
a)Express the total cost in terms of K and Q.
b)Derive the expression of marginal cost of capital.
c)Derive the long-run cost function...

For each of the following production
functions,
• Write an equation and graph the isoquant for Q =
100.
• Find the marginal rate of technical substitution and
discuss how MRTSLK changes as the ?rm uses more L, holding output
constant.
(c) Q(K,L) = LK + L

A pie shop has a production function given by Q =
30K1/3L1/3, where Q is the number of
pies produced per hour, K is the number of ovens (which is
fixed at 8 in the short run), and L is the number of
employed workers. How many pies can be produced per hour with 27
workers in the short run?
Question 9 options:
200
150
220
180
Question 10 (2 points)
The production function for an automobile industry is given...

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),...

A firm produces an output with the production function Q = KL,
where Q is the number of units of output per hour when the firm
uses K machines and hires L workers each hour. The marginal
products for this production function are MPK= L and MPL= K. The
factor price of K is 4 and the factor price of L is 2. The firm is
currently using K = 16 and just enough L to produce Q = 32....

The production function for a firm is given by q = L0.75 K0.3
where q denotes output; L and K labor and capital inputs
. (a) Determine marginal product of labor. Show whether or not
the above production function exhibits diminishing marginal
productivity of labor.
(b) Calculate the output (or production) elasticity with respect
to labor.
c) Determine the nature of the Return to Scale as exhibited by
the above production function. Show and explain all
calculations

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,...

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