Q: If the production function is $$Y = A K$$^{0.5}$$ L$$^{0.5}$$ and A = 2$, K = 100$, L = 25$, what is the value of Y$?

$$Y = 2 \times 10 \times 5 = 100$$

Question 1

Which of the following best describes the concept of diminishing marginal returns in the context of the neoclassical growth model?

Accepted Answer

Increasing one factor of production while holding others fixed leads to a smaller increase in output with each additional unit.

Question 2

Given the Cobb-Douglas production function $$Y = A K^\alpha L$$^{1-\alpha}$$, if both capital K$ and labor L$ are doubled, what happens to output Y$?

Accepted Answer

Output $$Y is $$doubled.

Question 3

Suppose the level of technology $$A$$ increases while capital $$K$$ and labor $$L$$ remain constant in the production function $$Y = F(K, L; A). $$What is the effect on output $$Y$$?

Accepted Answer

Output $$Y$$ increases.

Question 4

If the marginal product of labor (MPL) is calculated as $$MPL(n) = Y(n) - Y(n-1)$$, what does a declining MPL as $$n$$ increases indicate?

Accepted Answer

Diminishing marginal returns to labor.

Question 5

In the neoclassical growth model, which of the following is NOT considered a basic input of production?

Accepted Answer

Government spending ($$G)$$

Question 6

If national saving increases, what is the most likely immediate effect on the real interest rate and investment, according to the study materials?

Accepted Answer

The real interest rate falls and investment rises.

Question 7

Given the production function $$Y = 2 \cdot 100$$^{0.5}$$ \cdot 113$$^{0.5}$$, what is the effect on output Y$ if both K$ and L$ are increased by a factor of 2?

Accepted Answer

Output $$Y$$ increases by a factor of 2.

Question 8

Which of the following best explains why output per worker ($$Y/L) $$remains unchanged when both capital ($$K) $$and labor ($$L) $$are scaled by the same factor in a production function with constant returns to scale?

Accepted Answer

Because output increases by the same proportion as inputs.

Question 9

Suppose an economy experiences a shift in investment demand. According to the study materials, what is the likely effect on the real interest rate and future potential output?

Accepted Answer

The real interest rate changes, and future potential output changes through its effect on investment.

Question 10

If output per worker ($$Y/L) $$falls as more labor is added while capital is fixed, what economic principle does this illustrate?

Accepted Answer

Diminishing marginal returns to labor.

Question 11

Which of the following equations represents the national income identity in a closed economy, as referenced in the study materials?

Accepted Answer

$$Y = C + I + G$$

Question 12

If the production function is $$Y = A K$$^{0.5}$$ L$$^{0.5}$$ and A = 2$, K = 100$, L = 25$, what is the value of Y$?

Accepted Answer

$$Y = 2 	imes 10 	imes 5 = 100$$

Question 13

Which of the following statements about constant returns to scale is correct?

Accepted Answer

Doubling all inputs doubles output.

Question 14

In the context of the neoclassical growth model, what is the primary role of technology ($$A) in $$the production function?

Accepted Answer

It increases output for given levels of capital and labor.

Question 15

If an economy increases its human capital ($$H) $$while holding physical capital ($$K) $$and labor ($$L) $$constant, what is the expected effect on output ($$Y$$)?

Accepted Answer

Output ($$Y) $$increases.

Question 16

Suppose the marginal product of labor (MPL) for the 10th worker is calculated as $$MPL(10) = Y(10) - Y(9). If$$ $$Y(10) = 89.6$$ and $$Y(9) = 87.0$$, what is $$MPL(10)$$?

Accepted Answer

$$MPL(10) = 2.6$$

Question 17

Which of the following best describes the effect of increasing investment on long-run economic growth, according to the study materials?

Accepted Answer

It increases the growth rate of future potential output.

Question 18

If an economy starts with $$K = 27$$ and $$L = 64$$, and both are doubled, what happens to output $$Y$$ under constant returns to scale?

Accepted Answer

Output $$Y is $$doubled.

Question 19

Which of the following is a direct implication of diminishing marginal returns to labor when capital is fixed?

Accepted Answer

Each additional worker contributes less output than the previous one.

Question 20

If the aggregate production function is $$Y = F(K, L, H; A)$$, which of the following would NOT increase output $$Y$$?

Accepted Answer

A decrease in physical capital ($$K)$$

Long-Run Economic Growth: The Neoclassical Growth Model

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