Economics 308, Fall 2015 Problem Set 1: Convergence

This assignment will have you solve out some simple problems related to our discussion of economic growth during the nineteenth century. You are welcome to use a spreadsheet but it is not required. You must explain your answers in enough detail to make them clear, but make sure your answers are focused and to the point. This is not an essay.

Please turn your answers to the TA before class.

Answer all questions below in all four sections. If you took an introductory macroeconomics class, I and II will look familiar. Short-answer questions are exactly that; they can can be answered in a paragraph or two. Long essays are neither required nor encouraged.

I. Growth Rates [14 points]

The number of slurms in Wormulon is 50 in 1400, 80 in 1800, and 120 in 1850.

(1) [4 points] Compute the percentage change in slurms over the two periods defined by these three dates.

(2) [6 points] Compute the average rate of growth in slurms for the period 1400-1800, 1800-1850, and 1400-1850.

(3) [4 points] Your answer for the growth rate in the period 1400-1850 in question (2) is not equal to the growth rate in either sub-period. Comment.

II. Total Factory Productivity [26 points]

Total factory productivity (TFP) and factor accumulation are useful concepts that help us better understand patterns of economic growth. It is especialy important in economic history since economic growth and its determinants are central issues in the field.

In this section, we will work with an equation of the following form:

where the delta symbols denote changes (so that Y/Y describes the percentage change in Y ). Y is output, L, K, and T are labor, capital, and resource inputs, respectively. R is the growth-accounting residual or the measure of TFP. a, b, and c are weights.

(1) [4 points] Your 14 year-old sisted is a highly intelligent person but knows nothing about economics. Explain this equation to her.

(2) [4 points] Why do we need the weights a,b, and c?

Consider the experience of the economy summarized in the following table.

Year Y L K T

1 20 40 40 80

2 100 50 100 82

3 150 60 180 82

(3) [4 points] Assume a = 0.3,b = 0.5,c = 0.2. Compute R for growth between year 1 and year 2, and for growth between year 2 and year 3.

(4) [8 points] Assume a = 0.3,b = 0.6,c = 0.1. Compute R again for growth between year 1 and year 2, and for growth between year 2 and year 3. Why is your answer different? Explain in economic terms.

(5) [6 points] Suppose I gave you data on Y , the weights, and the labor input L. Sketch, in words, a method for speculating about R without getting it too wrong.

III. Solow and Growth Rates [35 points]

For this section, we are working with the Solow model where capital and output are in per-capita terms. We are also restricting ourselves, for the moment, to the version that makes every country converge to the same level.

The Solow model has two basic equations:

y = k? (1) k = sy (n + )k (2)

where y is output per labor, k is capital per labor, s is the savings rate, is the rate of depreciation, and n is the rate of population growth.

(1) [2 points] In words, explain what each equation means in economic terms.

(2) [4 points] Now find an expression for the steady-state values of y and k. Hint: substitute equation (1) into (2) and set k to zero.

(3) [4 points] Explain why this is a steady state? If you lived in this economy, what would it look like?

(4) [20 points; 5 points each] The following statements are true or false. Say which, then explain why.

(a) If country A is growing faster than country B, then we know A is poorer than B.

(b) If A is growing faster than B, then we we know that it has a higher savings rate than B.

(c) Suppose A has faster population growth than B. Then, in the steady state, A will be poorer thanB in per-capita terms.

(d) Suppose that country A has positive poulation growth and B has negative population growth.Explain what the Solow model implies about these two countries. Then think about what reality might tell us. Explain the limitations of the simple Solow model this comparison implies.

(5) [5 points] Suppose there are two countries in a Solow world. One is much wealthier than the other. If it were possible for the rich country to invest in the poor, what would happen? Use the model to describe this.

IV. Solow and Conditional Convergence [25 points]

In this section, assume we are in a Solow world where each country has different parameters. We don’t know which parameters are different.

(1) [15 points; 5 points each] More true/false and explain:

(a) In country A, the absolute amount of investment is greater each year than in country B. Thismust mean that B is wealthier than A.

(b) Ceteris paribus, if ?is greater in A than in B, it means A is wealthier per capita.

(c) Suppose we know that A and B will converge to different steady states, but we do not know anything more than that. If we see A growing faster than B, what can we conclude? What other information might allow us to say something more?

(2) [10 points] Now use these models to structure an understanding of the following sets of facts.

(i) The U.S. had per-capita income similar to that of Britain in 1800. By 1930, the U.S. per capitaincome was much higher than Britain’s.

(ii) In 1820, German per-capita income was much lower than that of Britain. By the late 1920s,German incomes were higher. Today they are about the same again.

(iii) The U.S. growth has always been “low but steady,” about 2 percent per year without muchdeviation from that.

Note: there is no one “right” story to tell about these facts, but there are those that use economic reasoning correctly. Feel free to say what you would need to be precise, and clearly state any assumptions you make.

Economics 308, Fall 2015 Problem Set 1: Convergence

This assignment will have you solve out some simple problems related to our discussion of economic growth during the nineteenth century. You are welcome to use a spreadsheet but it is not required. You must explain your answers in enough detail to make them clear, but make sure your answers are focused and to the point. This is not an essay.

Please turn your answers to the TA before class.

Answer all questions below in all four sections. If you took an introductory macroeconomics class, I and II will look familiar. Short-answer questions are exactly that; they can can be answered in a paragraph or two. Long essays are neither required nor encouraged.

I. Growth Rates [14 points]

The number of slurms in Wormulon is 50 in 1400, 80 in 1800, and 120 in 1850.

(1) [4 points] Compute the percentage change in slurms over the two periods defined by these three dates.

(2) [6 points] Compute the average rate of growth in slurms for the period 1400-1800, 1800-1850, and 1400-1850.

(3) [4 points] Your answer for the growth rate in the period 1400-1850 in question (2) is not equal to the growth rate in either sub-period. Comment.

II. Total Factory Productivity [26 points]

Total factory productivity (TFP) and factor accumulation are useful concepts that help us better understand patterns of economic growth. It is especialy important in economic history since economic growth and its determinants are central issues in the field.

In this section, we will work with an equation of the following form:

where the delta symbols denote changes (so that Y/Y describes the percentage change in Y ). Y is output, L, K, and T are labor, capital, and resource inputs, respectively. R is the growth-accounting residual or the measure of TFP. a, b, and c are weights.

(1) [4 points] Your 14 year-old sisted is a highly intelligent person but knows nothing about economics. Explain this equation to her.

(2) [4 points] Why do we need the weights a,b, and c?

Consider the experience of the economy summarized in the following table.

Year Y L K T

1 20 40 40 80

2 100 50 100 82

3 150 60 180 82

(3) [4 points] Assume a = 0.3,b = 0.5,c = 0.2. Compute R for growth between year 1 and year 2, and for growth between year 2 and year 3.

(4) [8 points] Assume a = 0.3,b = 0.6,c = 0.1. Compute R again for growth between year 1 and year 2, and for growth between year 2 and year 3. Why is your answer different? Explain in economic terms.

(5) [6 points] Suppose I gave you data on Y , the weights, and the labor input L. Sketch, in words, a method for speculating about R without getting it too wrong.

III. Solow and Growth Rates [35 points]

For this section, we are working with the Solow model where capital and output are in per-capita terms. We are also restricting ourselves, for the moment, to the version that makes every country converge to the same level.

The Solow model has two basic equations:

y = k? (1) k = sy (n + )k (2)

where y is output per labor, k is capital per labor, s is the savings rate, is the rate of depreciation, and n is the rate of population growth.

(1) [2 points] In words, explain what each equation means in economic terms.

(2) [4 points] Now find an expression for the steady-state values of y and k. Hint: substitute equation (1) into (2) and set k to zero.

(3) [4 points] Explain why this is a steady state? If you lived in this economy, what would it look like?

(4) [20 points; 5 points each] The following statements are true or false. Say which, then explain why.

(a) If country A is growing faster than country B, then we know A is poorer than B.

(b) If A is growing faster than B, then we we know that it has a higher savings rate than B.

(c) Suppose A has faster population growth than B. Then, in the steady state, A will be poorer thanB in per-capita terms.

(d) Suppose that country A has positive poulation growth and B has negative population growth.Explain what the Solow model implies about these two countries. Then think about what reality might tell us. Explain the limitations of the simple Solow model this comparison implies.

(5) [5 points] Suppose there are two countries in a Solow world. One is much wealthier than the other. If it were possible for the rich country to invest in the poor, what would happen? Use the model to describe this.

IV. Solow and Conditional Convergence [25 points]

In this section, assume we are in a Solow world where each country has different parameters. We don’t know which parameters are different.

(1) [15 points; 5 points each] More true/false and explain:

(a) In country A, the absolute amount of investment is greater each year than in country B. Thismust mean that B is wealthier than A.

(b) Ceteris paribus, if ?is greater in A than in B, it means A is wealthier per capita.

(c) Suppose we know that A and B will converge to different steady states, but we do not know anything more than that. If we see A growing faster than B, what can we conclude? What other information might allow us to say something more?

(2) [10 points] Now use these models to structure an understanding of the following sets of facts.

(i) The U.S. had per-capita income similar to that of Britain in 1800. By 1930, the U.S. per capitaincome was much higher than Britain’s.

(ii) In 1820, German per-capita income was much lower than that of Britain. By the late 1920s,German incomes were higher. Today they are about the same again.

(iii) The U.S. growth has always been “low but steady,” about 2 percent per year without muchdeviation from that.

Note: there is no one “right” story to tell about these facts, but there are those that use economic reasoning correctly. Feel free to say what you would need to be precise, and clearly state any assumptions you make.