Question

(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.

Answer #1

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)...

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 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...

A? Cobb-Douglas production function
A. exhibits constant returns to scale.
B. exhibits decreasing returns to scale.
C. exhibits increasing returns to scale.
D. can exhibit? constant, increasing, or decreasing returns to
scale.

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

A firm produces output according to the production function.
Q=sqrt(L*K) The
associated marginal products are MPL = .5*sqrt(K/L) and MPK =
.5*sqrt(L/K)
(a) Does this production function have increasing, decreasing, or
constant marginal
returns to labor?
(b) Does this production function have increasing, decreasing or
constant returns to
scale?
(c) Find the firm's short-run total cost function when K=16. The
price of labor is w and
the price of capital is r.
(d) Find the firm's long-run total cost function...

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

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?...

5. Which of the following statements with respect to a
Cobb-Douglas production function is not true?
a. MPK and MPL depend on the quantity of both K and L used
b. the exponent of each input refers to its output
elasticity
c. the sum of the exponents determine the type of returns the
production function exhibits
d. the sum of the exponents represent the expansion path

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.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 6 minutes ago

asked 10 minutes ago

asked 16 minutes ago

asked 17 minutes ago

asked 19 minutes ago

asked 44 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago