Question

1. A. The Cobb-Douglas production function, f(x,y)=40x^1/4y^3/4, describes the production of a company for which each unit of labor costs $100 and each unit of capital costs $125. For a new project, the company has allocated $60,000 for labor and capital. Find the amount of money that the company should allocate to labor and capital to maximize production.

B. The marketing department of a business has determined that the demand for a product can be modeled by p=(50/(square root of x)). The cost of producing x units is given by C=0.50x+500. What price will yield a maximum profit?

Answer #1

Consider the Cobb-Douglas production function, f ( x , y ) = 50
x 4 5 y 1 5 , where f ( x , y )represents the number of units of a
product produced using x units of labor and y
units of capital.
A. Compute the marginal productivities of labor and
capital when 32 unit of labor and 1 units of capital are
used.
B. Use the marginal productivities to approximate the
change in the number of units...

The Cobb-Douglas production function for an automobile
manufacturer is
f(x, y) =
100x0.6y0.4,
where x is the number of units of labor and y
is the number of units of capital. Estimate the average production
level if the number of units of labor x varies between 300
and 350 and the number of units of capital y varies
between 375 and 400. (Round your answer to two decimal places.)

Suppose a Cobb-Douglas Production function is given by the
following:
P(L,K)=10L0.9K0.1
where L is units of labor, K is units of capital, and
P(L,K)P(L,K) is total units that can be produced with this
labor/capital combination. Suppose each unit of labor costs $400
and each unit of capital costs $1,200. Further suppose a total of
$600,000 is available to be invested in labor and capital
(combined).
A) How many units of labor and capital should be "purchased" to
maximize production subject...

Suppose a Cobb-Douglas Production function is given by the
following: P(L, K) = (50L^(0.5))(K^(0.5)) where L is units of
labor, K is units of capital, and P(L, K) is total units that can
be produced with this labor/capital combination. Suppose each unit
of labor costs $300 and each unit of capital costs $1,500. Further
suppose a total of $90,000 is available to be invested in labor and
capital (combined).
A) How many units of labor and capital should be "purchased"...

A firm’s production is represented by the following Cobb-Douglas
function: ? = ?^2/3?^1/3. The rental rate, r, of capital is given
by $200 and the price of labor is $100.
a) For a given level of output, what should be the ratio of
capital to labor in order to minimize costs?
b) How much capital and labor should be used to produce those
300 units?
c) What is the minimum cost of producing 300 units?
d) What is the short...

A firm’s production is represented by the following Cobb-Douglas
function: ? = ?^2/3?^1/3. The rental rate, r, of capital is given
by $200 and the price of labor is $100.
a) For a given level of output, what should be the ratio of
capital to labor in order to minimize costs?
b) How much capital and labor should be used to produce those
300 units?
c) What is the minimum cost of producing 300 units?
d) What is the short...

Given the Cobb-Douglas production function q = 2K 1 4 L 3 4 ,
the marginal product of labor is: 3 2K 1 4 L 1 4 and the marginal
product of capital is: 1 2K 3 4 L 3 4 .
A) What is the marginal rate of technical substitution
(RTS)?
B) If the rental rate of capital (v) is $10 and the wage rate
(w) is $30 what is the necessary condition for cost-minimization?
(Your answer should be...

33 II) A firm’s production is represented by the following
Cobb-Douglas function: ? = ?^1/3 ?^2/3. The rental rate, r, of
capital is given by $100 and the price of labor is $200.
a. For a given level of output, what should be the ratio of
capital to labor in order to minimize costs?
b. How much capital and labor should be used to produce those
300 units?
c. What is the minimum cost of producing 300 units?
d. What...

3. The White Noise Corporation has estimated the following
Cobb-Douglas production function using monthly observations for the
past two years:
ln Q = 2.485 + 0.50 ln K + 0.50 ln L + 0.20 ln N
where Q is the number of units of output, K is the number of
units of capital, L is the number of unit of labor, and N is the
number of units of raw materials. With respect to the above
results, answer the following...

Problem 1. Consider the Cobb-Douglas production function f(x, y)
= 12x 0.4y 0.8 .
(A) Find the intensities (λ and 1 − λ) of the two factors of
production. Does this firm have decreasing, increasing, or constant
returns to scale? What percentage of the firm’s total production
costs will be spent on good x?
(B) Suppose the firm decides to increase its input bundle (x, y)
by 10%. That is, it inputs 10% more units of good x and 10%...

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