Question

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. Diminishing marginal product of capital

B. Increasing returns to scale

C. Decreasing returns to scale

Answer #1

Answer-1. **Correct option is 'B'**

The aggregate production function shows a(n) **increasing**
relationship between **capital stock**
and output. When the capital stock increases, holding everything
else fixed, the production function shifts up. Then for a given
amount of labor, the amount of output produced in the economy
increases.

Answer-2. **Correct option is 'C'**

**The slope of the aggregate production function imply
diminishing returns to scale.** Because both country have
identical production function, same amount of capital stock but the
labour amount is not same, so flexible labor supply initially give
increasing returns but after a point it give diminishing returns.
The law of diminishing returns to scale states that as one input
variable increased, there is a point at which the marginal increase
in output begins to decrease, holding all other input constant.

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.

The Per-worker production function shows the relationship
between the amount of output per worker and capital per worker.
This curve is not linear but increases at a decreasing rate.
Why?
If a worker has more and more capital, the additional capital
will not be used as well as the previous capital, resulting in a
smaller increase in output than previous units of capital.
Too much capital will result in inefficient production
If a worker has more capital, that worker will...

A country has 100 units of labor (L) and production functions x
= (Lx)^0.5 and y = 4Ly, where Lx and Ly describe the labor
allocation. When the country divides its labor equally between
producing x & y, what is the rate of product transformation
(slope) for the PPF?
a. 49.3
b. 56.7
c. 61.1
d. 71.0

4.. Suppose the aggregate production function is given by Y =
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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.

The production function Q = 20K0.75L0.25 exhibits
A decreasing returns to scale.
B constant returns to scale.
C increasing returns to scale.
D increasing, then diminishing returns to scale.
E negative returns to scale.

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...

2. A firm has the following linear production function:
q = 5L + 2K
a. Does this firm’s production function exhibit diminishing
returns to labor?
b. Does this production function exhibit diminishing returns to
capital?
c. Graph the isoquant associated with q = 20.
d. What is the firm’s MRTS between K and L?
e. Does this production technology exhibit decreasing, constant,
or increasing returns to scale?

Find the marginal product of each input, determine if the
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Consider the following production function Y=z*(a*K + (1-a)*N)
where z represents total factor productivity, a is a parameter
between 0 and 1, K is the level of capital, and N is labor. We want
to check if this function satisfies our basic assumptions about
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1. Does this production function exhibit constant returns to
scale? Ex- plain
2. Is the marginal product of labor always positive? Explain
3. Does this function exhibit diminishing marginal product of
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The production function of good x is as follows: Q =
(L^0.5)(K^0.4)
a. Does this production function have increase, constant or
decreasing returns to scale? _______(Answer either IRS, DRS or
CRS)
b. Calculate the slope of the isoquant when the entrepreneur is
producing efficiently with 10 laborers and 20 units of capital.
Slope = ______(Answer as a fraction or decimal.)
c. If we increase the amount of labor we use in our production
process from 10 to 15 units, how...

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