Queens College, CUNY - ECON 201

CHAPTER 5: The Solow Growth Model

TRUE/FALSE

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

 

                                

 

2. The Solow model of economic growth endogenizes investment.

 

                                

 

3. In the Solow model, the equation of capital accumulation is .

 

 

 

4. In the Solow model, if gross investment is greater than capital depreciation, the economy accumulates new capital.

 

 

 

5. In the Solow model, if gross investment is equal to capital depreciation, the economy accumulates new capital.

 

                                

 

6. In the Solow model, it is assumed that a constant fraction of capital depreciates in each period.

 

 

 

7. For any given saving rate, depreciation rate, and production function, changing the initial capital stock yields a different steady state.

 

                                

 

8. In the Solow model, defining as the saving rate and Y_t as output, consumption is given by .

 

                                

 

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

stock.

 

                                

 

10. In the Solow model, the saving rate is an endogenous variable.

 

                                

 

11. If we define the saving rate as , output as , and the depreciation rate as , and if , the economy is in the steady state.

 

                                

 

12. If is the saving rate, is the production function, and is the depreciation rate, the growth of capital can be expressed as .

 

 

 

13. A change in the capital stock, , can be expressed as a function of the saving rate, , output , the capital stock, K_t, and the depreciation rate by , as .

 

                                

 

 

14. In the steady state, capital accumulation is zero.

 

 

 

15. In the steady state, capital accumulation is positive.

 

                                

 

16. In the Solow model, we generally assume that the capital depreciation rate is the same across all countries.

 

 

 

 

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

 

                                

 

18. The Solow model assumes the saving rate decreases as income increases.

 

                                

 

19. In the steady state, output per person is growing.

 

                                

 

20. A decline in the saving rate will cause the steady state level of output and capital to rise.

 

                                

 

21. 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.

 

 

 

22. Immediately following the increase in the investment rate, output grows rapidly. As the economy approaches its new steady state, the growth rate gradually declines.

 

 

 

23. The key difference between the Solow and production models is that the Solow model endogenizes the saving rate.

 

                                

 

24. The productivity parameter, , plays a larger role in the Solow model than it does in the production model.

 

 

 

25. A surprising result of the Solow model is that capital accumulation cannot serve as the engine of growth in the long run.

 

 

26. If we include population growth in the Solow model, we can model this concept by thinking of population growth as capital depreciation per person.

 

 

 

SHORT ANSWER

 

1. What are the key assumptions of the Solow growth model?

 

 

 

2. Show the transition dynamics in the Solow model if .

 

 

 

 

3. Suppose that rather than the Cobb-Douglas production function being given as , it is given by . Find the steady-state level of capital and output in the Solow model.

 

 

 

4. Given a production function , if , and :

1. Calculate the steady-state level of capital and output.
2. Does the above production function exhibit constant returns to scale, or does it exhibit diminishing marginal returns? Explain, and define the difference between these two concepts.

 

 

 

 

5. Consider the data in Figure 5.8, which shows the growth rates for three countries that were involved in World War II. How does the basic Solow model explain the trends in growth rates for each of these countries?

 

 

 

6. 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