Question

In the Cobb-Douglas production function :

the marginal product of labor (L) is equal to β1

the average product of labor (L) is equal to β2

if the amount of labor input (L) is increased by 1 percent,

the output will increase by β1 percent if the amount of Capital input (K) is increased by 1 percent,

the output will increase by β2 percent

C and D

Answer #1

Ans: C and D

**Explanation:**

The Cobb-Douglas production function represents the relationship between two or more inputs,i.e., capital and labor and the quantity of outputs that can be produced.

The Cobb-Douglas production function basically represents constant returns to scale, because B1 + B2 = 1. So, in the Cobb-Douglas production function, if the amount of labor input (L) is increased by 1 percent, the output will increase by β1 percent if the amount of Capital input (K) is increased by 1 percent, the output will increase by β2 percent.

Thus, the answer is C and D.

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...

1. Using the Cobb-Douglas production function:
Yt =
AtKt1/3Lt2/3
If K = 27, L = 8 A = 2, and α = 1/3, what is the value of Y?
(For K and L, round to the nearest whole number) ______
2. If Y = 300, L = 10, and α = 1/3, what is the marginal product
of labor? ______
3. Using the values for Y and α above, if K = 900, what is the
marginal product of capital?...

1. Consider the Cobb-Douglas production function Q = 6 L^½ K^½
and cost function C = 3L + 12K. (For some reason variable "w" is
not provided)
a. Optimize labor usage in the short run if the firm has 9 units
of capital and the product price is $3.
b. Show how you can calculate the short run average total cost
for this level of labor usage?
c. Determine “MP per dollar” for each input and explain what the
comparative...

1. Assume the following Cobb-Douglas production function:
Y=0.5K0.2L0.8. If
L=100,
a. What is the marginal product of
capital?
b. With your answer in (a), can you
prove diminishing marginal product of capital?
c. Estimate real capital income
d. Estimate the share of real capital
income
d. Estimate the share of real capital
income

Consider the following Cobb-Douglas production function: y(K,L)
= 2K^(0.4)*L^(0.6), where K denotes the amount of capital and L
denotes the amount of labour employed in the production
process.
a) Compute the marginal productivity of capital, the marginal
productivity of labour, and the MRTS (marginal rate of technical
substitution) between capital and labour. Let input prices be r for
capital and w for labour. A representative firm seeks to minimize
its cost of producing 100 units of output.
b) By applying...

for a firm with Cobb-Douglas production function
q = f (k, L) = k ^ (1/2) L ^ (1/2)
calculate the total, average and marginal cost.

Assuming a Cobb-Douglas production function with constant
returns to scale, then, as L rises with K and A constant, it will
be the case
Group of answer choices
Both the marginal product of labour and the marginal product of
capital will fall
Both the marginal product of labour and the marginal product of
capital will rise
The marginal product of labour will rise and the marginal
product of capital will fall
The marginal product of labour will fall and the...

You are given this estimate of a Cobb-Douglas production
function: Q = 10K0.6L0.8 A. Calculate the output elasticities of
capital and labor. (Note: As shown on p. 300, for the Cobb-Douglas
production function Q = 10KaLb the output elasticity of capital is
EK = (%ΔQ/%ΔK) = a and the output elasticity of labor is EL =
(%ΔQ/%ΔL) =
b. B. Using what you found in Part (A), by how much will output
increase if the firm increases capital by 10...

(a) Show that the following Cobb-Douglas production function,
f(K,L) = KαL1−α, has constant returns to scale.
(b) Derive the marginal products of labor and capital. Show
that you the MPL is decreasing on L and that the MPK is decreasing
in K.

a) Show that the following Cobb-Douglas production function,
f(K,L) = KαL1−α, has constant returns to scale.
(b) Derive the marginal products of labor and capital. Show
that you the MPL is decreasing on L and that the MPK is decreasing
in K.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 25 minutes ago

asked 29 minutes ago

asked 59 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago