Exam 5: The Solow Growth Model

If South Korea's steady-state GDP per worker is higher than that in the Philippines, you might conclude that the investment rate in South Korea is higher than in the Philippines.

A change in the capital stock, ÄK_t, can be expressed as a function of the saving rate, $\bar { s }$ , output, $F \left( K _ { t } , \bar { L } \right)$ , the capital stock, K_t, and the depreciation rate, $\bar { d }$ , by:

In the steady state, gross investment is less than capital depreciation.

If the depreciation and saving rates are constant, the economy eventually will settle in the steady state in the Solow model because of:

Suppose you are given the data for Brazil and Portugal. In Brazil, the saving rate is 0.1 and the depreciation rate is 0.1, while in Portugal the saving rate is 0.2 and the depreciation rate is 0.1. Using the Solow model, you conclude that in the steady state:

If we define the saving rate as $\bar { s }$ , output as $F \left( K _ { t } , \bar { L } \right)$ , and the depreciation rate as $\bar { d }$ , and if $\bar { s } F \left( K _ { 2 } , \bar { L } \right) - \bar { d } K _ { t } = 0$ , the economy is:

In the Solow model, if we assume that capital depreciation rates are the same across all countries, differences in per capita output can be explained by:

In the Solow model, in every period, a fraction of total output ________ next period's capital stock, which ________.

In the Solow model, the ________ plays a ________ role than it does in the standard production function model.

In the Solow model, if, in the absence of any shocks, the capital stock remains at K* forever, this rest point is called the:

If South Korea's steady-state GDP per worker is higher than that of the Philippines, you might conclude that:

Refer to the following figure when answering Figure 5.5: Solow Diagram -Consider the Solow model exhibited in Figure 5.5. Which of the following is/are true? i. If 1 denotes Country 1 and 2 denotes Country 2, Country 1 has a higher saving rate. ii. If 1 denotes Country 1 and 2 denotes Country 2, Country 1 has a lower depreciation rate. iii. If 1 denotes Country 1 and 2 denotes Country 2, Country 2 has a lower steady state.

Refer to the following figure when answering Figure 5.3: Solow Diagram -In Figure 5.3, at K₁, the difference between $\bar { s } Y$ and $\bar { d } K$ Is ________ and the difference between Y and $\bar { s } Y$ Is ________.

You are asked to make comparisons of two pairs of countries. The first pair are the Latin American countries of Chile and Argentina; the second pair are France and Germany. You are given the following information: the average saving rate in Argentina is 23.3 percent, in Chile it is 28.7 percent, in France it is 21.1 percent, and in Germany, 20.8 percent. Assuming the countries are identical in every other way, which country would the Solow model predict to have the higher per capita real GDP? However, you find out the steady state real per capita GDP in each of the countries is $13,300 in Argentina, $12,500 in Chile, $31,300 in France, and $34,000 in Germany. What is the primary factor that the simple Solow model uses to describe these differences? Give an example.

If the production function is given by $Y = \bar { A } K _ { t } ^ { 1 / 3 } \bar { L } ^ { 2 / 3 }$ , the saving rate, s, is 20 percent, the depreciation rate, $\bar d$ , is 10 percent, and $\bar { A } = \bar { L } = 1$ , the steady-state level of output is:

In the corn farm example, corn can be used as either saving or depreciation.

In the simple Solow model, we assume:

If we define $\bar { s } _ { 1 }$ and $\bar { s } _ { 2 }$ As the saving rates in Countries 1 and 2, respectively, $\bar { d } _ { 1 } = \bar { d } _ { 2 }$ As the depreciation rates in Countries 1 and 2, respectively, $\bar { A } _ { 1 }$ And $\bar { A } _ { 2 }$ As productivity in Countries 1 and 2, respectively, and the production function per worker is $y _ { t } = \bar { A } \bar { K } _ { t } ^ { 1 / 3 }$ In both countries, the Solow model predicts the ratio of GDP per worker in Country 1 relative to Country 2 is:

The key difference between the Solow model and the production model is:

The amount of capital in an economy is a flow, while new investment is a stock.