Question 1

Suppose the aggregate production function for an economy is given by $$Y = AF(K, N)$$, where $$A is $$total factor productivity (TFP), $$K is $$capital, and $$N is $$labor. If $$A$$ increases due to a technological innovation, what is the most likely effect on output $$Y$$, holding $$K$$ and $$N$$ constant?

Accepted Answer

Output $$Y$$ will increase because the same inputs are used more efficiently.

Question 2

Which of the following best describes the concept of diminishing marginal product of capital in the context of the Cobb-Douglas production function $$Y = AK$$^{0.3}$$N^{0.7}$?

Accepted Answer

As more capital $$K is $$added, holding labor $$N$$ constant, the additional output produced by each extra unit of $$K$$ decreases.

Question 3

If the production function exhibits constant returns to scale, what happens to output $$Y if $$both capital $$K$$ and labor $$N$$ are doubled?

Accepted Answer

Output $$Y$$ will also double.

Question 4

Given the Cobb-Douglas production function $$Y = AK$$^{0.3}$$N^{0.7}$, what is the marginal product of labor (MPN)?

Accepted Answer

$$MPN = 0.7AK$$^{0.3}$$N^{-0.3}$

Question 5

A negative supply (productivity) shock, such as a natural disaster, affects the production function $$Y = AK$$^{0.3}$$N^{0.7}$ by:

Accepted Answer

Decreasing $$A$$, which shifts the production function downward.

Question 6

Suppose in a given year, the growth rates of output $$Y$$, capital $$K$$, and labor $$N$$ are 4%, 2%, and 1% respectively. If the Cobb-Douglas production function is $$Y = AK$$^{0.3}$$N^{0.7}$$, what is the approximate growth rate of total factor productivity $$A$?

Accepted Answer

1.1%

Question 7

Which of the following is NOT considered a factor of production in the aggregate production function $$Y = F(K, N, E, M; A)$$?

Accepted Answer

Government spending

Question 8

In the Cobb-Douglas production function $$Y = AK$$^{a}$$N^{1-a}$$, the exponents on $$K$$ and $$N$ represent:

Accepted Answer

The shares of output paid to capital and labor in competitive markets.

Question 9

If a country experiences an improvement in managerial practices, how would this be reflected in the Cobb-Douglas production function $$Y = AK$$^{0.3}$$N^{0.7}$?

Accepted Answer

An increase in $$A$$, representing higher total factor productivity.

Question 10

Suppose the marginal product of capital (MPK) is given by $$MPK = \frac{\partial Y}{\partial K}. $$For the Cobb-Douglas production function $$Y = AK$$^{0.3}$$N^{0.7}$$, what happens to $$MPK as$$ $$K$$ increases, holding $$N$ constant?

Accepted Answer

$$MPK$$ decreases due to diminishing marginal returns.

Question 11

Which of the following real-world events would most likely cause a positive supply (productivity) shock in the production function $$Y = AK$$^{0.3}$$N^{0.7}$?

Accepted Answer

The introduction of a new, more efficient manufacturing technology.

Question 12

If the production function is $$Y = AK$$^{0.3}$$N^{0.7}$$ and both $$K$$ and $$N$$ are increased by 10%, by what percentage does output $$Y$ increase?

Accepted Answer

10%

Question 13

Which of the following statements about total factor productivity (TFP) is TRUE?

Accepted Answer

TFP captures the effectiveness with which capital and labor are used in production.

Question 14

Suppose the output of the Canadian economy is well approximated by $$Y = AK$$^{0.3}$$N^{0.7}. If$$ $$A$$ increases by 5%, $$K$$ increases by 2%, and $$N$$ increases by 1%, what is the approximate percentage increase in $$Y$?

Accepted Answer

5.7%

Question 15

Which of the following best explains why the Cobb-Douglas production function is often used in macroeconomics?

Accepted Answer

It exhibits constant returns to scale and matches empirical data on factor shares.

Question 16

If the marginal product of labor (MPN) is $$MPN = \frac{\partial Y}{\partial N}$$, what is the effect of increasing $$N on$$ $$MPN in $$the Cobb-Douglas production function $$Y = AK$$^{0.3}$$N^{0.7}$$, holding $$K$ constant?

Accepted Answer

$$MPN$$ decreases due to diminishing marginal returns.

Question 17

Which of the following is an example of a negative supply shock in the context of the aggregate production function?

Accepted Answer

A major supply chain disruption that reduces the efficiency of production.

Question 18

In the Cobb-Douglas production function $$Y = AK$$^{0.3}$$N^{0.7}$$, if $$K = 100$$, $$N = 200$$, and $$A = 2$$, what is the value of $$Y$ (rounded to the nearest integer)?

Accepted Answer

Y = 325

Question 19

Which of the following best describes the role of the 'residual' in estimating total factor productivity (TFP) in the Cobb-Douglas production function?

Accepted Answer

It is the portion of output growth not explained by capital and labor growth.

Aggregate Production, Productivity, and Employment in Macroeconomics

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