Question

**A firm discovers that when it uses K units of capital
and L units of labor it is able to**

** produce q=4K^1/4
L^3/4 units of output.**

a) **Calculate the MPL, MPK and MRTS**

**b) Does the production function (q=4K^1/4 L^3/4) exhibit
constant, increasing or decreasing returns to scale and
why?**

**c) Suppose that capital costs $10 per unit and labor can
each be hired at $40 per unit and the firm uses 225 units of
capital in the short run. How much labor is used and what is the
short-run total cost to produce 600 units of output?**

**d) Continue to assume that capital and labor can be
hired at $40 per unit for labor and $10 for capital. In the long
run if the firm produces 600 units of output, how much labor and
capital will be used and what is the LR Total cost of
production?**

Answer #1

A firm discovers that when it uses K units of capital and L
units of labor, it is able to produce X= L^1/4*K^3/4 units of
output 1. Continue to assume that capital and labor can each be
hired at $1 per unit. Show that in the long run, if the firm
produces 24 units of output, it will employ 16 units of capital and
81 units of labor. What is the long-run total cost to produce 12
units of output?...

A firm uses two inputs, capital K and labor L, to produce output
Q that can be sold at a price of $10. The production function is
given by Q = F(K, L) = K1/2L1/2 In the short run, capital is fixed
at 4 units and the wage rate is $5, 1. What type of production
function is F(K, L) = K1/2L1/2 ? 2. Determine the marginal product
of labor MPL as a function of labor L. 3. Determine the...

Assume that a profit maximizer firm uses only two inputs, labor
(L) and capital (K), and its production function is f(K,L) = K2 x
L. Its MRTS of capital for labor (i.e., how many units of capital
does he want to give up one unit of labor) is given by MRTS = MPL /
MPK = K / (2L) a) Assume that this firm wants to spend $300 for the
inputs (total cost of factors of production). The wage per...

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 uses capital and labor to produce output according to
the production ? = 4√??
(a) Find the marginal product of labor (MPL) and marginal
product of capital (MPK).
(b) If the wage w=$1/labor-hr. and the rental rate of capital
r=$4/machine-hr., what is the
least expensive way to produce 16 units of output?
(c) What is the minimum cost of producing 16 units?
(d) Show that for any level of output, q, the minimum cost of
producing q is...

When capital increases by ?K units and labor increases
by ?L units, output (?Y) increases by:
A.
MPL + MPK units.
B.
(MPL × ?K) + (MPK × ?K)
units.
C.
(MPK × ?K) + (MPL × ?L)
units.
D.
?K + ?L units.

When the market wage = $ 60 and the marginal product of labor
(MPL ) = 6 and the price of capital ( c)) is $ 10, then
at optimal level of labor and capital, the marginal product of
capital (MPK ) is
10
6
1
0.17
Suppose a firm is operating in both a perfectly competitive
product market and perfectly labor market. The firm’s short run
production is Q = L2; where Q is output and L is labor,...

2. A firm combines labor (L) and capital (K) to produce output
(Q). The price of one unit
of labor is 50 and the price of one unit of capital is 20. This
firm is producing in the
short run (remember that in the short run there is one fixed
resource, in this case,
capital). Complete the following information for this firm
L K Q TVC TFC TC ATC AVC AFC MC
0 20 0 -
1 18
2 60...

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 a firm that sells output and buys labor in a
competitive market. The firm’s production function is given by
q=K1/2L1/2 where q is the quantity of output,
K is the amount of capital, and L is the number of labor
hours. The marginal product of labor is
MPL=1/2K1/2L-1/2 .Suppose the amount of
capital is fixed at 100 units (i.e., short-run).
a.) If the output can be sold for $10 per unit and labor can be
purchased for $5 per...

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