Question

1. Assume the following Cobb-Douglas production function:
*Y=0.5**K**0.2**L**0.8*. 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

Answer #1

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?...

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

Which is/are incorrect about the Cobb-Douglas production
function: Y equals K to the power of alpha L to the power of 1
minus alpha end exponent (0 < alpha < 1 )? All are correct it
increases in both K and L the share of total income that goes to
capital and labor depend on the amount of K and L it exhibits
diminishing marginal returns to both K and L it is constant returns
to scale

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. 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

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...

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...

Cobb-Douglas Production Function & Cost of
Production
A firm’s production function is given as –
q =
2K0.4N0.6
What kind of returns to scale does this production technology
exhibit? Justify your answer.
Find out the expression for the marginal product of labor.
Find out the expression for the marginal product of
capital.
Find out the expression for MRTS.

6.7 The production function
Q=KaLb where 0≤ a, b≤1 is called a Cobb-Douglas production
function. This function is widely used in economic research. Using
the function, show the following:
a. The production function in Equation 6.7 is a special case of
the Cobb-Douglas.
b. If a+b=1, a doubling of K and L will double q.
c. If a +b < 1, a doubling of K and L will less than double
q.
d. If a +b > 1, a doubling...

Consider the Cobb-Douglas production function F (L, K) =
(A)(L^α)(K^1/2) , where α > 0 and A > 0.
1. The Cobb-Douglas function can be either increasing, decreasing
or constant returns to scale depending on the values of the
exponents on L and K. Prove your answers to the following three
cases.
(a) For what value(s) of α is F(L,K) decreasing returns to
scale?
(b) For what value(s) of α is F(L,K) increasing returns to
scale?
(c) For what value(s)...

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