Question

1. Using the Cobb-Douglas production function:

Y_{t} =
A_{t}K_{t}^{1/3}L_{t}^{2/3}

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? Express your answer as a percentage. _______

4. For the Cobb-Douglas production function, if α = 1/5, what would labor’s share of output be?________

5. For the Cobb-Douglas production function, if A = 2 and Y =100, what would Y be if A increases to a value of 3?

______

Answer #1

(1) Plugging in given values,

Y = 2 x (27)^{1/3} x (8)^{2/3} = 2 x 3 x 4 =
**24**

(2) Plugging in given values,

300 = 2 x (K)^{1/3} x (10)^{2/3}

150 = (K)^{1/3} x (10)^{2/3}

Taking (3/2)-th root on both sides,

(150)^{3/2} = (K)^{1/2} x 10

Squaring,

(150)^{3} = K x 100

K = (150 x 150 x 150) / 100 = 33,750

**MPL =**
Y/L
= 2 x (2/3) x (K/L)^{1/3} = (4/3) x (33,750 /
10)^{1/3} = (4/3) x (3,375)^{1/3} = (4/3) x 15 =
**20**

(3) Plugging in given values,

300 = 2 x (900)^{1/3} x (L)^{2/3}

150 = (900)^{1/3} x (L)^{2/3}

Taking (3/2)-th root on both sides,

(150)^{3/2} = (900)^{1/2} x L

Squaring,

(150)^{3} = L^{2} x 900

L^{2} = (150 x 150 x 150) / 900 = 3,750

L = 61.24

**MPK =**
Y/K
= 2 x (1/3) x (L/K)^{2/3} = (2/3) x (61.24 /
900)^{2/3} = (2/3) x (0.068)^{2/3} = (2/3) x 0.1667
= 0.1111 = **11.11%**

**NOTE:** As per Answering Policy, first 3
questions are answered.

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)...

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.

2. Consider a Cobb-Douglas production function Q = A . L^a . K^b
. Answer the following in terms of L, K, a, b
(a) What is the marginal product of labour ?
(b) What is the marginal product of capital ?
(c) What is the rate of technical substitution (RTS L for
K)?
(d) From the above what is the relation between K L and RT
SL,K?
(e) What is the relation between ∆ K L ∆RT SL,K (f)...

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...

(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.

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

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

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...

Normalize the cobb douglas production function Y = F (K,L) =
K1/2L1/2 in terms of output per unit of
labor. Note that this function does not have technology change.
Your answer should be in terms of y = f(k) =
Answer is y = (K/L)1/2 = k1/2
Please show step by step how to do this including the
derivate and exponent laws you use

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 12 minutes ago

asked 31 minutes ago

asked 51 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago