Question

Given the Cobb-Douglas production function for Mabel’s factory

Q = (L0.4) * (K0.7)

a) Based on the function above, does Mabel’s factory experiencing

economies or diseconomies of scale? Explain.

b) If the manager wished to raise productivity by 50% and planned to

increase capital by 25%, how much would she have to increase her labor

to reach that desired production level?

Answer #1

Q=L^0.4*K^0.7

Above function is Cobb Douglas of form Q=L^(alpha)*K^(beta) and
if **alpha+beta>1** then increasing return to scale
and **alpha+beta=1** then constant return to scale;
**alpha+beta<1** then decreasing return to
scale

In our case 0.4+0.7=1.1>1

ANswer for b)

New Q=1.5*Old Q

New K=1.25* Old K

New Q=(New K)^0,7*(New L)^0.4

Old Q=K^0.7*L^0.4

New K)^0,7*(New L)^0.4=1.5*K^0.7*L^0.4

(1.25*K)^0.7*(New L)^0.4=1.5*K^0.7*L^0.4

New L^0.4=(1.5/1.2)^0.7*L^0.4

New L^0.4=1.17*L^0.4

New L=1.17^(0.25)*L

New L=1.04*L

Hence Labor should be increased by 4%

Consider the following Cobb-Douglas Production Function for
Mauricio’s Machines Inc, a U.S. manufacturer of electronic
precision tools:
Q=(L*0.4)+(K*0.7)
Explain why a Cobb-Douglas production is indeed a
representation of reality?
Based on the function above, is Mauricio’s Machines’ business
experiencing Economies of Scale or Diseconomies of Scale? Please
explain your answer.
this is all the provided information so please answer the
question

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.

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...

Suppose country A has the following Cobb-Douglas production
function q = AKαE 1−α . Suppose country A receives large foreign
direct investments in capital (FDI)
(a) How does an increase in FDI affect labor productivity in
country A? How would wages respond in the short-run?
(b) In the long run, what are the implications of FDI on
potential future immigration out of country A?

2. Assume that a manufacturer faces a Cobb-Douglas production
function, q=40K^0.5L^0.5
where q is output per period, L is labor, K is capital. The
market price of labor (w) is $50 per unit and the price of capital
(r) is $200 per unit.
a. Specify and illustrate graphically the short-run MPl and APl
for L = 5 to 30 units (assume that the level of capital is 25; use
increments of 5 units of labor). Is this firm operating in...

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...

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...

Assume a Cobb-Douglas production function of the form:
q=10L0.09K0.47. What type of returns to scale LOADING... does this
production function exhibit? In this instance, returns to scale
equal ?. (Enter a numeric response using a real number rounded to
two decimal places.)

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

1. In previous problem, the given Cobb-Douglas
production function was Q = 6 L½
K½ and the cost function was given as:
C = 3L + 12K. For $384
of total cost, the optimum labor usage was determined to be 64, and
capital of 16.
a. If the cost
function now changes to C = 3L + 18K, it implies that the total
cost will become $480. Compute the new level of total cost for Q =
192. Can...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 8 minutes ago

asked 13 minutes ago

asked 18 minutes ago

asked 37 minutes ago

asked 46 minutes ago

asked 51 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago