contestada

In the economy of Solovia, the owners of capital get two-thirds of national income, and the workers receive one-third. a. The men of Solovia stay at home performing household chores, while the women work in factories. If some of the men started working outside the home so that the labor force increased by 5 percent, what would happen to the measured output or the economy? Does labor productivity-defined as output per worker-increase, decrease, or stay the same? Does total factor productivity increase, decrease, or stay the same? b. In year 1, the capital stock was 6, the labor input was 3, and output was 12. In year 2, the capital stock was 7, the labor input was 4, and output was 14. What happened to total factor productivity between the two years?

Respuesta :

tutorconsortium623

a.  A five percent increase in labor input will increase output by 1.67 percent in Solovia.

The labor productivity-defined as output per worker will fall for 3.34 percent.

Total factor productivity growth is zero.

b. Total factor productivity will fall by approximately 5.6 percent.

What is labor productivity?

An economy's hourly output is ascertained by labor productivity. It specifically shows how much real gross domestic product (GDP) is generated in a given hour of labor. Savings, investments in new technology, and human capital are the three key drivers of labor productivity growth.

Calculation:

a. Since total output depends on productivity, labor and capital, it can be written as,

[tex]\frac{\Delta Y}{Y}=\frac{\alpha \Delta K}{K}+(1-\alpha )\frac{\Delta L}{L}+\frac{\triangle A}{A}[/tex]

There's a 5% increase in labor, therefore,

[tex]\begin{array}{l}\frac{\triangle K}{K}=\frac{\triangle A}{A}=0 \\\\\frac{\triangle Y}{Y}=\frac{1}{3} \cdot 0.05 \\\\\frac{\triangle Y}{Y}=0.0167\end{array}[/tex]

Therefore, a 5% increase in labor increases output by 1.67%.

Labor productivity is,

[tex]\begin{array}{c}\frac{\triangle Y}{Y}=\frac{\triangle\left(\frac{Y}{L}\right)}{\frac{Y}{L}}-\frac{\triangle L}{L} \\\frac{\triangle\left(\frac{Y}{Y}\right)}{\frac{Y}{L}}=0.0167-0.05=-0.0334\end{array}[/tex]

Therefore, labor productivity falls by 3.34%.

Now, to find the total factor productivity change,

[tex]\begin{array}{c}\frac{\triangle A}{A}=\frac{\triangle Y}{Y}-\frac{\alpha \triangle K}{K}-(1-\alpha) \frac{\triangle L}{L} \\\\\frac{\triangle A}{A}=0.0167-0-\frac{1}{3} \cdot 0.05=0\end{array}[/tex]

Therefore, there is no change in total factor productivity.

b. Between the years capital stock grows by [tex]\frac{1}{6}[/tex] input grows by [tex]\frac{1}{3}[/tex] and output grows by [tex]\frac{1}{6}[/tex] .

[tex]\begin{array}{c}\frac{\triangle A}{A}=\frac{\triangle Y}{Y}-\frac{\alpha \triangle K}{K}-(1-\alpha) \frac{\triangle L}{L} \\\\\frac{\triangle A}{A}=\frac{1}{6}-\frac{2}{3} \cdot \frac{1}{6}-\frac{1}{3} \cdot \frac{1}{3} \\\\\frac{\triangle A}{A}=\frac{3}{18}-\frac{2}{18}-\frac{2}{18} \\\\\frac{\triangle A}{A}=-\frac{1}{18}=-0.056\end{array}[/tex]

Therefore, total productivity falls by 5.6%.

To learn more about labor productivity:

https://brainly.com/question/6430277

#SPJ4

Otras preguntas