Seminar Questions part 1

Question 1

List at least three reasons why higher GDP per capita does not necessarily imply higher welfare. Does this mean we should not care that much about cross-country income differences? Explain why or why not.

Answer 1

• Higher GDP might be brought about by a higher labor supply and less leisure time
• Higher levels of production might cause higher levels of pollution, which might decrease utility
• Higher GDP might raise individual aspirations so that a given amount of consumption might generate less utility
• Human welfare depends on many factors that are not directly captured by GDP, such as health, education, life expectancy, weather.
• Still, we care greatly about cross-country income differences since GDP appears to be strongly correlated with alternative measures incorporating some of the factors listed above (while being at the same time easier to measure and compare across countries compared to such measures). Moreover, a country’s productive capacity is likely to be a key factor in generating improvements in several welfare-relevant domains, such as health and educational opportunities.

Question 2

(a) Write down an expression for the equilibrium wage and rental rate of capital. Represent graphically the equilibrium in the market for labour and capital.

Answer 2

• W* = (1-a)Y*/L*
• r* = a(Y*/L*)

Question 3

(b) Assume now that the government introduces an employment subsidy S so that firms pay only a fraction s of the employees’ wages. How are the equilibrium levels of labor, capital, the wage rate, and the rental rate of capital affected? Show both analytically and graphically.

Answer 3

Question 4

(c) Assume now instead of that the government introduces a tax on revenues T How are the equilibrium levels of labor, capital, the wage rate, and the rental rate of capital affected. Show both analytically and graphically.

Answer 4

Question 5

Answer 5

Question 6

Explain intuitively (in a couple of sentences) why, in the context of the Solow model, capital accumulation alone cannot be a source of long-run economic growth.

Answer 6

Capital accumulation does not generate sustained economic growth because there are decreasing marginal returns to capital in the production process. As a consequence of those, investment generates smaller and smaller relative increases in the capital stock over time, while at the same time a constant fraction of the capital stock depreciates away every period. At some point, depreciation is large enough to perfectly undo the effect of new investment, and growth has to stop.

Question 7

Consider an economy on the steady state of the Solow model. Suppose that suddenly an earth- quake destroys part of the capital stock. How are capital per worker, output per worker, the wage rate and the rental rate of capital affected in the short- and long-run? Explain both graphically and intuitively.

Answer 7

• Capital per worker - This decreases when the shock hits, and then starts to increase in the long run when the economy starts to move towards a steady state.
• Output per worker - This capital per worker evolution follows the output per worker evolution, it initially falls and then starts to increase.
• The wage rate is given by w = (1-a)Yt/Lt, therefore a fall in Yt due to a fall in the capital stock will lead to a fall in the wage rate, and then as the economy converges to a steady-state the wage rate will start to increase.
• The rental rate of capital is given by r=a(Yt/Kt), therefore a fall in output will also lead to a fall in the rental rate of capital, and then as the economy converges to a steady-state the rental rate of capital will start to increase.

Question 8

1. Consider an economy on the steady state of the Solow model. Suppose that suddenly an earthquake destroys part of the capital stock. How are capital per worker, output per worker, the wage rate and the rental rate of capital affected in the short- and long-run? Explain both graphically and intuitively.

Answer 8

• Capital stock starts to grow as Investment > Depreciation and continues to grow until a steady-state is reached.
• Capital per worker falls aswell as output per worker as they both follow the same pattern.
• Lower Yt leads to a lower Wt, as shown by the equation.
• Lower Yt also leads to a fall in the rental rate of capital.

Question 9

Explain intuitively (in a couple of sentences) why, in the context of the Solow model, capital accumulation alone cannot be a source of long-run economic growth.

Answer 9

• This is because capital exhibits decreasing marginal returns.
• The accumulation of capital increases growth, whilst a constant fraction is depreciated each year.
• At some point, due to diminishing marginal returns, the depreciation will be large enough to perfectly undo the effect of new investment, and therefore long-run growth cannot be achieved.

Question 10

1. Are the following statements true or false? Motivate your answer.
   (a) According to the Solow model, policies that increase the saving rate always improve welfare.
   (b) In the Solow model, an exogenous increase in the labor force affects aggregate GDP only temporarily.
   (c) A development accounting exercise and the calibration of the Solow model both suggest that cross-country gaps in GDP per worker are mostly due to differences in TFP.

Answer 10

(A) FALSE. An increase in the saving rate will increase output per worker in the long-run but might decrease consumption (which is what households care about).

(B) False. It permanently increases GDP while temporarily reduces GDP per worker. An increase in Lt increases Yt as Yt = F(K,L), however at the same time an increase in Lt reduces capital per worker, kt/lt, and therefore also GDP per worker. The economy after this then starts to transition into a new steady-state with Kt, kt, yt, and Yt all growing along with the transition into a new steady state. In the steady-state kt and yt are back to their pre-shock levels, while Kt and Yt are permanently higher.

(C) True. The development accounting shows that the empirical variation in capital per worker is small compared to the overall variation in GDP. Overall, showing TFP is the main driver of cross-country gaps in economic performance.

Question 11

Does the Solow model predict that currently, poor countries will eventually catch up with currently rich countries? Explain why or why not.

Answer 11

• It depends. The solo model predicts conditional convergence, which is conditional on if the countries have a similar value for the parameters (s,A,d).
• If the countries do not have a similar value of these parameters then they won’t converge to a steady-state.

Question 12

What is the accumulation of the capital equation?

Answer 12

• Kt+1 = sYt + (1-d)Kt
• d = the depreciation rate, so 1-d is the amount of capital that is left in period t that hasn’t depreciated.

Question 13

Write an expression for GDP per worker in the steady-state, Y* as a function of exogenous parameters only

Answer 13

Question 14

Write an expression for consumption per worker in the steady-state, C* as a function of exogenous parameters only

Answer 14

Question 15

What is known as the ‘golden rule’ saving rate?

Answer 15

• a/1-a = s/1-s
• The golden saving rate =a (s=a)

Question 16

What does Romer argue about ideas and objects?

Answer 16

• Romer argues that objects are rivalrous, while ideas are nonrivalrous. This means that due to the nonrivalrous nature, an idea can generate a greater than constant return to scale as one persons use does not affect the other persons use.

Question 17

State the solo residual and give 2 limitations of the solo residual

Answer 17

• At = Yt / Kt^a Lt^1-a
• Yt is difficult to measure as prices and quantity change over time making it extremely difficult to capture all changes.
• Yt doesn’t capture the value of nonmonetary things such as IT technologies, as they are difficult to measure.