Question 1

The marginal product of the labor curve represents the labor supply curve.

Accepted Answer

The marginal product of labor curve is a measure of the output produced by each additional unit of labor. The labor supply curve, on the other hand, represents the amount of labor that workers are willing to supply at each wage rate. These are two different curves and cannot be used interchangeably.

Question 2

In the aftermath of the Black Death in the fourteenth century, wages in Europe were higher than before the Black Death because millions of people died.

Accepted Answer

With a significant reduction in the labor force due to the massive death toll caused by the Black Death, there was a higher demand for laborers, resulting in increased wages.

Question 3

If the U.S. total factor productivity is 1.00 and China's is 0.33, then the U.S. capital per worker is 67 percentage points more productive than China's.

Accepted Answer

Total factor productivity measures the efficiency of inputs (such as labor and capital) in producing output. Therefore, a higher total factor productivity indicates that a country can produce more output with the same amount of inputs. If the US has a total factor productivity of 1.00 and China has a total factor productivity of 0.33, it means that the US can produce 3 times as much output as China using the same amount of inputs. Given this, it is likely that the US capital per worker is more productive than China's by a significant margin, making statement A true.

Question 4

Consider two countries, A and B. If each country produces using identical production functions, but y_A > y_B and k_A = k_B, the total factor productivity of country A equals that of B.

Accepted Answer

The given inequality y_A > y_B implies that country A produces more output per unit of input than country B, despite having the same level of capital. This means that country A has a higher total factor productivity than country B. Therefore, the statement in the question is false.

Question 5

One explanation of differences in total factor productivity is differences in labor's share of GDP.

Accepted Answer

Differences in total factor productivity (TFP) are primarily attributed to variations in technology, innovation, efficiency, and institutional structures across countries, rather than differences in labor's share of GDP. Labor's share of GDP reflects the distribution of income between labor and capital, not the efficiency or productivity of these factors.

Question 6

The two main inputs we consider in our production function model are labor and land.

Accepted Answer

The two main inputs typically considered in our production function model are labor and capital, not land.

Question 7

Consider two countries, A and B. If each country produces using identical production functions, but y_A = y_B and k_A = k_B, the total factor productivity of country A equals that of B.

Accepted Answer

The total factor productivity of a country depends on its production function and its inputs, including physical capital (k) and labor (y). If both countries have identical production functions and inputs, then their total factor productivity should be equal. Therefore, the statement is true.

Question 8

In the production function $Y = F ( K , L ) = \bar { A } \bar { K } ^ { 1 / 3 } L ^ { 2 / 3 }$ 
, $\bar { A }$ 
represents a productivity parameter.

Accepted Answer

In the given production function, $\bar { A }$ is a constant that represents the level of technology or productivity, affecting how efficiently inputs $K$ (capital) and $L$ (labor) are transformed into output $Y$.

Question 9

If you have data on per capita GDP and capital per worker, to find total factor productivity you can use the equation $\bar { A } = y / k ^ { 1 / 3 }$ 
, if capital's share of GDP is one-third.

Accepted Answer

The equation $\bar { A } = y / k ^ { 1 / 3 }$ is derived from the Cobb-Douglas production function, where capital's share of GDP is one-third, allowing us to solve for total factor productivity (TFP) given per capita GDP (y) and capital per worker (k).

Question 10

A production function of the form $Y = K ^ { 2 } L ^ { 1 - a }$ 
exhibits constant returns to scale.

Accepted Answer

The production function exhibits constant returns to scale because doubling both capital and labor inputs will double output. This is because the exponent sum of K and L is 1, which means that a proportional change in both inputs will result in the same proportional change in output.

Question 11

If you have data on per capita GDP and capital per worker, to find total factor productivity you can use the equation $\bar { A } = y / k ^ { 1 / 3 }$ 
, if capital's share of GDP is two-thirds.

Accepted Answer

The answer of If you have data on per capita...

Question 12

The production function of the form $Y = K ^ { 1 / 3 } L ^ { 1 / 3 }$ 
exhibits constant returns to scale.

Accepted Answer

The production function $Y = K^{1/3} L^{1/3}$ exhibits decreasing returns to scale because the sum of the exponents (1/3 + 1/3 = 2/3) is less than 1.

Question 13

A production function of the form $Y = K ^ { 2 } L ^ { 1 - a }$ 
is called the Cobb-Douglas production function.

Accepted Answer

The given statement is true because the Cobb-Douglas production function is a specific type of production function that has the form $Y = K ^ { 2 } L ^ { 1 - a }$, where Y is output, K is capital, L is labor, and a is a constant.

Question 14

If the marginal product of capital equals the rental rate of capital, firms should not hire any more capital.

Accepted Answer

If the marginal product of capital equals the rental rate of capital, it means that the additional production that can be obtained by hiring one more unit of capital is equal to the cost of renting that unit of capital. Therefore, the firm is indifferent between hiring one more unit of capital or not, as the additional revenue generated by that unit is exactly offset by the cost of renting it. Hence, the firm would not have any incentive to hire any more capital.

Question 15

The production function of the form $Y = K ^ { 1 / 2 } L ^ { 1 / 2 }$ 
exhibits constant returns to scale.

Accepted Answer

The production function $Y = K^{1/2} L^{1/2}$ exhibits constant returns to scale because if both inputs $K$ and $L$ are scaled by a factor $t$, the output $Y$ is also scaled by $t$, i.e., $ (tK)^{1/2} (tL)^{1/2} = t(K^{1/2} L^{1/2}) $.

Question 16

If the production function is given by $Y = K ^ { 1 / 3 } L ^ { 2 / 3 }$ 
, then labor's share of GDP is one-third.

Accepted Answer

In the given Cobb-Douglas production function, labor's share of GDP is represented by the exponent of $L$, which is $2/3$, not one-third.

Question 17

If the marginal product of labor equals the wages, firms should hire more workers.

Accepted Answer

When the marginal product of labor equals the wage rate, a firm maximizes profit by not hiring additional workers, as the cost of hiring one more worker (the wage) equals the additional revenue generated by that worker (the marginal product). Hiring more workers beyond this point would decrease profit.

Question 18

Exogenous variables are predetermined by the model builder.

Accepted Answer

Exogenous variables are variables that are predetermined by the model builder and are not affected by other variables in the model.

Question 19

If the production function is given by $Y = K ^ { 1 / 3 } L ^ { 2 / 3 }$ 
, the marginal product of capital is (1/3)(Y/K).

Accepted Answer

The marginal product of capital (MPK) is the partial derivative of the production function with respect to capital $K$. Differentiating $Y = K^{1/3}L^{2/3}$ with respect to $K$ gives $\frac{\partial Y}{\partial K} = \frac{1}{3}K^{-2/3}L^{2/3}$. Simplifying, this is $\frac{1}{3}\left(\frac{Y}{K}\right)$.

Question 20

If the production function is $Y = K ^ { 1 / 3 } L ^ { 2 / 3 }$ 
, then in per worker terms, it can be written as $y = K ^ { 1 / 3 } / L$ 
.

Accepted Answer

The per worker production function is derived by dividing the production function by labor $L$, resulting in $y = (K/L)^{1/3}$, not $K^{1/3}/L$.

Quiz 4: A Model of Production

The marginal product of the labor curve represents the labor supply curve.

In the aftermath of the Black Death in the fourteenth century, wages in Europe were higher than before the Black Death because millions of people died.

If the U.S. total factor productivity is 1.00 and China's is 0.33, then the U.S. capital per worker is 67 percentage points more productive than China's.

Consider two countries, A and B. If each country produces using identical production functions, but yA > yB and kA = kB, the total factor productivity of country A equals that of B.

One explanation of differences in total factor productivity is differences in labor's share of GDP.

The two main inputs we consider in our production function model are labor and land.

Consider two countries, A and B. If each country produces using identical production functions, but yA = yB and kA = kB, the total factor productivity of country A equals that of B.

In the production function Y=F(K,L)=AˉKˉ1/3L2/3Y = F ( K , L ) = \bar { A } \bar { K } ^ { 1 / 3 } L ^ { 2 / 3 }Y=F(K,L)=AˉKˉ1/3L2/3 , Aˉ\bar { A }Aˉ represents a productivity parameter.

If you have data on per capita GDP and capital per worker, to find total factor productivity you can use the equation Aˉ=y/k1/3\bar { A } = y / k ^ { 1 / 3 }Aˉ=y/k1/3 , if capital's share of GDP is one-third.

A production function of the form Y=K2L1−aY = K ^ { 2 } L ^ { 1 - a }Y=K2L1−a exhibits constant returns to scale.

If you have data on per capita GDP and capital per worker, to find total factor productivity you can use the equation Aˉ=y/k1/3\bar { A } = y / k ^ { 1 / 3 }Aˉ=y/k1/3 , if capital's share of GDP is two-thirds.

The production function of the form Y=K1/3L1/3Y = K ^ { 1 / 3 } L ^ { 1 / 3 }Y=K1/3L1/3 exhibits constant returns to scale.

A production function of the form Y=K2L1−aY = K ^ { 2 } L ^ { 1 - a }Y=K2L1−a is called the Cobb-Douglas production function.

If the marginal product of capital equals the rental rate of capital, firms should not hire any more capital.

The production function of the form Y=K1/2L1/2Y = K ^ { 1 / 2 } L ^ { 1 / 2 }Y=K1/2L1/2 exhibits constant returns to scale.

If the production function is given by Y=K1/3L2/3Y = K ^ { 1 / 3 } L ^ { 2 / 3 }Y=K1/3L2/3 , then labor's share of GDP is one-third.

If the marginal product of labor equals the wages, firms should hire more workers.

Exogenous variables are predetermined by the model builder.

If the production function is given by Y=K1/3L2/3Y = K ^ { 1 / 3 } L ^ { 2 / 3 }Y=K1/3L2/3 , the marginal product of capital is (1/3)(Y/K).

If the production function is Y=K1/3L2/3Y = K ^ { 1 / 3 } L ^ { 2 / 3 }Y=K1/3L2/3 , then in per worker terms, it can be written as y=K1/3/Ly = K ^ { 1 / 3 } / Ly=K1/3/L .

Consider two countries, A and B. If each country produces using identical production functions, but y_A > y_B and k_A = k_B, the total factor productivity of country A equals that of B.

Consider two countries, A and B. If each country produces using identical production functions, but y_A = y_B and k_A = k_B, the total factor productivity of country A equals that of B.

In the production function $Y = F ( K , L ) = \bar { A } \bar { K } ^ { 1 / 3 } L ^ { 2 / 3 }$ , $\bar { A }$ represents a productivity parameter.

If you have data on per capita GDP and capital per worker, to find total factor productivity you can use the equation $\bar { A } = y / k ^ { 1 / 3 }$ , if capital's share of GDP is one-third.

A production function of the form $Y = K ^ { 2 } L ^ { 1 - a }$ exhibits constant returns to scale.

If you have data on per capita GDP and capital per worker, to find total factor productivity you can use the equation $\bar { A } = y / k ^ { 1 / 3 }$ , if capital's share of GDP is two-thirds.

The production function of the form $Y = K ^ { 1 / 3 } L ^ { 1 / 3 }$ exhibits constant returns to scale.

A production function of the form $Y = K ^ { 2 } L ^ { 1 - a }$ is called the Cobb-Douglas production function.

The production function of the form $Y = K ^ { 1 / 2 } L ^ { 1 / 2 }$ exhibits constant returns to scale.

If the production function is given by $Y = K ^ { 1 / 3 } L ^ { 2 / 3 }$ , then labor's share of GDP is one-third.

If the production function is given by $Y = K ^ { 1 / 3 } L ^ { 2 / 3 }$ , the marginal product of capital is (1/3)(Y/K).

If the production function is $Y = K ^ { 1 / 3 } L ^ { 2 / 3 }$ , then in per worker terms, it can be written as $y = K ^ { 1 / 3 } / L$ .