Question

Suppose that a firm has the Cobb-Douglas production function Q = 12K ^ (0.75) L^ (0.25). Because this function exhibits (constant, decreasing, increasing) returns to scale, the long-run average cost curve is (upward-sloping, downward-sloping, horizontal), whereas the long-run total cost curve is upward-sloping, with (an increasing, a declining, a constant) slope.

Now suppose that the firm’s production function is *Q =
KL*. Because this function exhibits (constant, decreasing,
increasing) returns to scale, the long-run average cost curve is
(upward-sloping, downward-sloping, horizontal), whereas the
long-run total cost curve is upward-sloping, with (an increasing, a
declining, a constant) slope.

Answer #1

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.

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...

For each part of this question write down a Cobb-Douglas
production function with the returns to scale called for and
perform a proof for each that shows the production function has the
correct returns to scale.
Constant returns to scale
Decreasing returns to scale
Increasing returns to scale
Increasing returns to scale

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)...

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...

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.

(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 firm’s production is represented by the following Cobb-Douglas
function: ? = ?^2/3?^1/3. The rental rate, r, of capital is given
by $200 and the price of labor is $100.
a) For a given level of output, what should be the ratio of
capital to labor in order to minimize costs?
b) How much capital and labor should be used to produce those
300 units?
c) What is the minimum cost of producing 300 units?
d) What is the short...

A firm’s production is represented by the following Cobb-Douglas
function: ? = ?^2/3?^1/3. The rental rate, r, of capital is given
by $200 and the price of labor is $100.
a) For a given level of output, what should be the ratio of
capital to labor in order to minimize costs?
b) How much capital and labor should be used to produce those
300 units?
c) What is the minimum cost of producing 300 units?
d) What is the short...

33 II) A firm’s production is represented by the following
Cobb-Douglas function: ? = ?^1/3 ?^2/3. The rental rate, r, of
capital is given by $100 and the price of labor is $200.
a. For a given level of output, what should be the ratio of
capital to labor in order to minimize costs?
b. How much capital and labor should be used to produce those
300 units?
c. What is the minimum cost of producing 300 units?
d. What...

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