Question

Find the marginal product of each input, determine if the production function has diminishing marginal product for each input, determine if the production function has constant, increasing, or decreasing returns-to-scale. f(x, y) = min{12x, 3y}.

Answer #1

Q = f(x, y) = min{12x, 3y}

Marginal product of x, MPx = dQ/dx = 12

Thus, MPx is constant and not diminishing because it is a constant
value.

Marginal product of y, MPy = dQ/dy = 3

Thus, MPy is constant and not diminishing because it is a constant
value.

Now, let x = tx and y = ty where t is a constant and t >
1.

So, Q' = f(tx, ty) = min{12tx, 3ty} = min{t(12x, 3y)} = tmin{12x,
3y} = tQ

Thus, we can see that power of t is 1 which means that there are
constant returns to scale.

For each of the following production functions, (i) sketch an
isoquant, (ii) indicate whether each marginal product is
diminishing, constant, or increasing points, and (iii) indicate
whether the production function shows constant, decreasing, or
increasing returns to scale.
A) Q = f(L, K) = L2K3
B) Q = f(L, K) = 2L +
6K
C) Q = f(L, K) = (minL, K) (1/2)

Suppose that the production function
y=f(x_1,x_2) (where: y is output level, x_1 is a
variable input and x_2 is a fixed input), is plotted in the (y,
x_1) space. According to economic theory, we would expect:
a. y to increase with x_1 at a decreasing rate,
due to increasing returns to scale.
b. y to increase with x_1 at an increasing
rate, due to diminishing returns to scale.
c. y to increase with x_1 at a decreasing rate,
due to...

The aggregate production function shows a(n) ________
relationship between ________ and output.
A. decreasing; capital stock
B. increasing; capital stock
C. constant; labor
D. decreasing; labor
Country X and Country Y have identical aggregate production
functions as shown below. The amount of capital stock available to
each country is also equal. However, Country X has LX amount of
labor supply while Country Y has LY amount of labor supply.
What does the slope of the aggregate production function
imply?
A....

Consider the following production function q
= K2 + L2.
Does this production function exhibit constant, increasing or
decreasing returns to scale?)
Find an expression for the marginal rate of technical
substitution. Does this production function exhibit diminishing
marginal rate of technical substitution? Explain

production function Consider a firm that produces a single
output good Y with two input goods: labor (L) and capital (K). The
firm has a technology described by the production function f : R 2
+ → R+ defined by f(l, k) = √ l + √ k, where l is the quantity of
labor and k is the quantity of capital. (a) In an appropriate
diagram, illustrate the map of isoquants for the firm’s production
function. (b) Does the...

Each of the following is a consequence of diminishing marginal
product except one, which one?
A. output increases at a decreasing rate as
units of the variable input are added.
B. marginal cost increases as the firm
increases production.
C. the firm’s total cost increases at an
increasing rate as the firm increases production.
D. output falls as units of the variable
input are added.

Wheat is produced according to the production function Q = 100
K^0.8 L^0.2
a. Beginning with a capital input of 4 and a labor input of 49,
show that the marginal product of labor and the marginal product of
capital are both decreasing.
b. Does this production function exhibit increasing, decreasing,
or constant returns to scale?
please explain in 4 sentences thank you!

Suppose the aggregate production function is given by Y =
K0.5L0.5. Does it have increasing, decreasing or constant returns
to scale? Show that the marginal products of capital and labour are
declining. Show that they are increasing in the input of the other
factor.

4.. Suppose the aggregate production function is given by Y =
K0.5L0.5. Does it have increasing, decreasing or constant returns
to scale? Show that the marginal products of capital and labour are
declining. Show that they are increasing in the input of the other
factor.

1) The production function Q =
50K0.25L0.25 exhibits
A. increasing returns to scale. B. constant returns to
scale.
C. decreasing returns to scale. Answer
D. increasing, then diminishing returns to scale.
E. negative returns to scale.
2) The production function Q =
50K0.25L0.75 exhibits
A. increasing, then diminishing returns to scale. B. increasing
returns to scale.
C. decreasing returns to scale.
D. constant returns to scale. Answer
E. negative returns to scale.
could you please explaing me the reason of...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 7 minutes ago

asked 8 minutes ago

asked 9 minutes ago

asked 10 minutes ago

asked 18 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