Growth96

Outline

Self Test

Lecture Notes

Problem Set on Economic Growth

Problem I (Growth Accounting) (Reccommended)

You have been appointed to head a Presidential Commission to study the effect of the transition to a market economy on the growth of real GDP in the Republic of Moldova. As part of that study you wish to asses the impact of economic reforms on the growth of total factor productivity. In order to do that, you must first estimate the growth rate of total factor productivity (TFP) in Moldova.

PART A: Analysis of the Moldovan Economy

Your devoted staff assembled the following information for you.:

FACTS ABOUT MOLDOVA FOR THE PERIOD 1990 -1995

Average rate of inflation 18.3%

Average annual rate of growth of the capital stock 3.0%

Average annual per capita vodka consumption 4 .1 liters

Average annual trade deficit $124,659,000

Average annual rate of growth of the labor force 1.2%

Average annual growth rate of the money supply 16.4%

Average annual growth of industrial production 8.4%

Average annual growth of agricultural production 1.1%

Average annual growth of Real GDP 3.15%

Average annual growth rate of the population 1.6%

Share of GDP going to the providers of capital . 25

Share of GDP spent on consumption . 74

Share of GDP going to the providers of labor .75

Share of GDP spent on imports .21

Average age of the labor force 37.8 years

Average weight of economics professors 89.7 kilos

Some of the information collected by your staff is useful. Some of it is not. Select the relevant data and answer the following questions: (In each case explain your calculations.)

1. What was the rate of growth of total factor productivity in Moldova during the period 1990 to 1995?

2. What proportion of the growth rate of the real GDP of Moldova in the period 1990 to 1995 was due to:

(a) The growth of the capital stock

(b) The growth of the labor force

3. At the current rates of growth, how many years would it take for Moldova to double its output of Real GDP?

4. At the current rates of growth, how many years would it take for Moldova to double its Real GDP per worker?

5. What will be the annual rate of growth of real GDP in Moldova if the annual rate of growth of the capital stock were increased from 3% to 6%? Why would a doubling of the rate of growth of the capital stock not result in a doubling in the rate of growth of real GDP?

6. What will be the annual rate of growth of real GDP per worker in Moldova if the annual rate of growth of the capital stock was increased from 3% to 6%?

7. What will be the annual rate of growth of real GDP in Moldova if the annual rate of growth of the capital stock is 3 % and annual rate of growth of the labor force was increased from 1.2% to 3%?

8. What will be the annual rate of growth of per capita real GDP in Moldova if the annual rate of growth of the capital stock is 3% and the annual rate of growth of the labor force was increased from 1.2% to 3%? Would the more rapid growth of the labor force improve the standard of living of the workers of Moldova?

9. What will be the annual rate of growth of real GDP in Moldova if the annual rate of growth of the capital stock were 3% and the annual rate of growth of the labor force was decreased from 1.5% to 0.0%?

10. What will be the annual rate of growth of real GDP per worker in Moldova if the annual rate of growth of the capital stock is 3% and the annual rate of growth of the labor force was decreased from 1.5% to 0.0%? Would the more rapid growth of the labor force improve the standard of living of the workers of Moldova?

Problem II.

The Independent Republic of Middlebury (IRM) is concerned about the fact that rate of economic growth has been declining every year since the Republic declared its independence. You have been hired as a macroeconomic consultant to advise the IRM on how to improve their long term growth performance. In order to analyze and explain the performance of the IRM economy, you decide to construct a neoclassical growth model.

Unfortunately the Government officials of the IRM find it extremely difficult to understand your analysis and your explanations because of the confusing system of notation that is generally used in constructing neoclassical growth models.

To help the officials of the IRM to understand the notation that you will use in your explanations, you have prepared the following guide.

A LAYMAN’S GUIDE TO NEOCLASSICAL-GROWTH-MODEL NOTATION

Per-worker variables:

k = K/L

y = Y/L

i = I/L

Per-unit-of-income variable:

s = S/Y

Per-unit-of-capital variable:

d = D/K

Annual rate-of-growth variables:

G_K= (K₁ - K₀) / K₀

G_k= (k₁ - k₀) / k₀

G_Y= (Y₁ - Y₀) / Y₀

G_y= (y₁ - y₀) / y₀

G_L= (L₁ - L₀) / L₀

Subscripts

g = gross (includes depreciation)

n = net (does not include depreciation)

gold = "golden age" variable

Superscripts

* = "steady state" variable

The following is an example of the notation:

i_{n gold}^* = net investment per worker in a "golden age steady state".

A. The Aggregate Production Function

You have decided to use a simple Cobb-Douglas aggregate production function. You estimated the exponents of the IRM aggregate production function using the "Joe Tham" method of multiple regression analysis (JT-OLS). Your estimate of the aggregate production function is as follows:

Y = K^1/2L^1/2

1. Derive the per worker production function.

2. Calculate the value of Real GDP per worker (y) for the following possible levels of the capital stock per worker (k): [1,4,9,16,25]

3. Graph the per-worker production function for the IRM.

B. The Current (1996) Economic Situation in the IRM

You have studied the economy of the IRM and have acquired the following information:

(a) The people of the IRM save 30 per cent of their income (s = .3).

(b) Because of the wear and tear of the production process, every year 10 per cent of the capital stock (K) wears out and must be replaced (d = .1).

(c) There are 4 thousand workers in the IRM. There has been no growth in the labor force and no growth is expected. You decide to measure the labor force in units of one thousand workers. (L = 4).

(d) The capital stock in the IRM in 1996 is 16 million dollars. You decide to measure the capital stock in units of one million dollars. (K = 16).

(e) There has been no change in the technology being used in the IRM and no technological changes are expected.

1. On the basis of this information show how you were able to calculate the following for the IRM in 1996:

(a) Capital per worker (k).

(b) Real GDP per worker (y)

(d) Consumption per worker (c)

(e) Gross investment per worker (i_g)

(f) Depreciation per worker (D/L)

(g) Net investment per worker (i_n)

2. In your report to the Government of the IRM you list both the per-worker and total values of the variables. What are the values of the following variables?

(a) Capital stock (K)

(b) Real GDP (Y)

(d) Total consumption (C)

(e) Gross investment (I_g)

(f) Depreciation (D)

(g) Net investment (I_n)

3. Construct a per-worker production function graph that illustrates the situation of the IRM in 1996. (Label the axes and the curves and indicate the levels of capital per worker, gross investment per worker and real GDP per worker.)

C. The Projected Economic Situation for 1997 and Beyond

1. On the basis of the calculations for 1996 show how you could calculate the following values for 1997:

(a) Capital per worker (k).

(b) Real GDP per worker (y)

(d) Consumption per worker (c)

(e) Gross investment per worker (i_g)

(f) Depreciation per worker (D/L)

(g) Net investment per worker (i_n)

2. In your report to the Government of the IRM you list both the per-worker and total values of the variables. What are the values of the following variables?

(a) Capital stock (K)

(b) Real GDP (Y)

(d) Total consumption (C)

(e) Gross investment (I_g)

(f) Depreciation (D)

(g) Net investment (I_n)

3. Will the standard of living be higher in 1997 than it was in 1996? Explain your answer.

4. Will the growth rate of capital per worker and the growth rate of real GDP per worker in 1998 be larger or smaller than in 1997. Explain your answer.

D. The Steady State of the IRM Economy

You have explained to the Government of the IRM (GIRM) that as the stock of capital per worker increases, the annual additions to real GDP per worker will decrease. The reason for this is the well known "Law of Diminishing Returns".

Smaller increments in real GDP per worker mean smaller increments in saving per worker. Ultimately the additional real GDP per worker will generate an amount of gross investment per worker that is only large enough to offset the depreciation per worker. At that point, the economy of the IRM will stop growing. It will have reached a "steady state".

The GIRM has asked you to forecast what the economic conditions will be like when the IRM reaches its "steady state".

1. Show how you made your calculations:

(a) Capital per worker (k^*).

(b) Real GDP per worker (y^*)

(d) Consumption per worker (c^*)

(e) Gross investment per worker (i_g^*)

(f) Depreciation per worker (D^*/L)

(g) Net investment per worker (i_n^*)

2. In your report to the GIRM you list both the per-worker and total values of the variables. What are the values of the following variables?

(a) Capital stock (K^*)

(b) Real GDP (Y^*)

(d) Total consumption (C^*)

(e) Gross investment (I_g^*)

(f) Depreciation (D^*)

(g) Net investment (I_n^*)

3. How large will be the following rates of growth? Explain your answers.

(a) Rate of growth of the capital stock (G_K^*)

(b) Rate of growth of the capital per worker (G_k^*)

(d) Rate of growth of real GDP per worker (G_y^*)

4. Construct a per-worker production function graph that illustrates the actual situation of the IRM in 1996 and the "steady state" values. (Label the axes and the curves and indicate the actual and "steady state" levels of capital per worker, gross investment per worker and real GDP per worker.)

5. What would happen to the capital stock per worker, investment per worker and real GDP per worker in 1997 if the economy of the IRM were already in a "steady state" in 1996?

E. An increase in the saving rate of the IRM.

The Chairman of the Council of Economic Advisors of the IRM is not happy with the projected "steady state" rate of growth of real GDP . He has suggested that the "steady state" rate of growth of real GDP can be significantly increased if the saving rate were increased from 30 per cent to 40 per cent of GDP (s = .4).

You have been asked to evaluate his proposal. To do this you calculate a new set of steady state values assuming a savings rate of 40% (s = .4).

1. Show how you calculated the following values:

(a) Capital per worker (k^*).

(b) Real GDP per worker (y^*)

(d) Consumption per worker (c^*)

(e) Gross investment per worker (i_g^*)

(f) Depreciation per worker (D^*/L)

(g) Net investment per worker (i_n^*)

2. In your report to the GIRM you list both the per-worker and total values of the variables. What are the values of the following variables?

(a) Capital stock (K^*)

(b) Real GDP (Y^*)

(d) Total consumption (C^*)

(e) Gross investment (I_g^*)

(f) Depreciation (D^*)

(g) Net investment (I_n^*)

3. How large will be the following rates of growth? Explain your answers.

(a) Rate of growth of the capital stock (G_K^*)

(b) Rate of growth of the capital per worker (G_k^*)

(d) Rate of growth of real GDP per worker (G_y^*)

4. Construct a graph that illustrates the "steady state" values for a 30 per cent savings rate and a 40 per cent savings rate. (Label the axes and the curves and indicate the two "steady state" levels of capital per worker, gross investment per worker and GDP per worker.)

5. What happened to the "steady state" values of the following variables when the savings rate was increased from .3 to .4?

(a) Capital stock per worker (k)

(b) Gross investment per worker (i_g)

(d) Real GDP per worker (y)

(e) Consumption per worker (c)

6. What will be the effect of increasing the savings rate from 30 per cent to 40 per cent on the following "steady state" growth rates ?

(a) Growth rate of the capital stock (G_K^*)

(b) Growth rate of capital worker (G_k^*)

(d) Growth rate of real GDP per worker (G_y^*)

7. Can the growth rate of the IRM economy be increased by increasing the savings rate? (Answer this question from both the short run and long run point of view.)

F. The Best Savings Rate for the IRM.

The President of the IRM wants to maximize the long run level of consumption of his people. He is sure that he can convince them to change their saving habits. But he is unsure whether he should ask them to increase or decrease their saving rate.

You are asked to help him decide on the best savings rate by calculating the "golden rule" level of capital per worker. Your staff mathematician informs you that since the real GDP per worker is equal to the square root of the capital stock per worker (y = k^1/2), the aggregate marginal product of capital per worker is as follows:

MPk = 1/(2*k^1/2)

1. Show how you calculated the following "golden rule" values for the IRM.

(a) Capital per worker (k_gold^*).

(b) Real GDP per worker (y_gold^*)

(d) Saving per worker (S^*_gold/L)

(e) Consumption per worker (c_gold^*)

(f) Gross investment per worker (i_{g gold}^*)

(g) Depreciation per worker (D_gold^*/L)

(h) Net investment per worker (i_{n gold}^*)

2. In your report to the GIRM you list both the per-worker and total values of the variables. What are the values of the following variables?

(a) Capital stock (K_gold^*)

(b) Real GDP (Y_gold^*)

(d) Total consumption (C_gold^*)

(e) Gross Investment (I_{g gold}^*)

(f) Depreciation (D_gold^*)

(g) Net investment (I_{n gold}^*)

3. How large will be the following "golden rule steady state" rates of growth? Explain your answers.

(a) Rate of growth of the capital stock (G_{K gold}^*)

(b) Rate of growth of the capital per worker (G_{k gold}^*)

(d) Rate of growth of real GDP per worker (G_{y gold}^*)

4. Construct a per-worker production function graph that illustrates the "steady state" values for a 30 per cent savings rate and the "golden rule" savings rate. (Label the axes and the curves and indicate the current "steady state" and "golden rule" levels of capital per worker, gross investment per worker, real GDP per worker and consumption per worker.)

5. What will happen to the "steady state" values of the following variables if the IRM adopts a "golden rule" savings rate?

(a) Capital stock per worker (k)

(b) Gross investment per worker (i_g)

(d) Real GDP per worker (y)

(e) Consumption per worker (c)

6. Should the President of the IRM call for a higher or a lower savings rate than the current savings rate (s = .3)? Explain your answer.

7. Assume that the President called for an increase in the saving rate to the "Golden Rule" level. Illustrate with a graph what will happen over time to (1) output per worker (2) consumption per worker and (3) Investment per worker.

E. The Effect of Labor Force Growth

In order to promote economic growth, the Chairman of the Council of Economic Advisors of the IRM has suggested that the IRM allow annual net labor immigration equal to 10 per cent of the labor force (G_L = .1).

You have been asked to determine whether his proposal would be good for the IRM . To do so you calculate the "steady state" of the IRM economy assuming a 10 per cent rate of labor force growth and the current saving rate (s = .3).

1. Assume that the economy of the IRM in 1996 is the same as was described in part B of this problem (s = .3). Calculate the following new "steady state" values for the IRM assuming a 10 per cent rate of growth of the labor force (G_L = .1). Explain your calculations:

(a) Capital per worker (k^*).

(b) Real GDP per worker (y^*)

(d) Consumption per worker (c^*)

(e) Gross investment per worker (i_g^*)

(f) Depreciation per worker (D^*/L)

(g) Net investment per worker (i_n^*)

2. How large will be the following rates of growth? Explain your answers.

(a) Rate of growth of the capital stock (G_K^*)

(b) Rate of growth of the capital per worker (G_k^*)

(d) Rate of growth of real GDP per worker (G_y^*)

3. Construct a per-worker production function graph that illustrates the "steady state" values before and after the labor force of the IRM started to grow. (Label the axes and the curves and indicate the "steady state" levels of capital per worker, gross investment per worker and GDP per worker, before and after the labor force started to grow.)

4. What will happen to the "steady state" values of the following variables if the growth rate of the IRM labor force increases from (G_L = 0.0) to (G_L = 0.1)?

(a) Capital stock per worker (k)

(b) Gross investment per worker (i_g)

(d) Real GDP per worker (y)

(e) Consumption per worker (c)

5. Caompare the following "steady state’ growth rates assuming no growth of the labor force and assuming a 10 per cent growth rate of the labor force

(a) Capital stock per worker (G_k^*)

(b) Real GDP per worker (G_y^*)

(d) Capital stock (G_K^*)

(e) Real GDP (G_Y^*)

6. Should the IRM accept the proposal of the Chairman of the Council of Economic Advisors of the IRM. Consider the following in making your decision:

(a) Will labor force growth increase the growth rate of the IRM?

(b) Will labor force growth increase or decrease the standard of living of the people of the IRM?

F. An Improvement in Technology

After completing your study of the IRM economy, you submit your final recommendations (and a very large bill for your services). You recommend against any growth in the population. Instead, you suggest that the IRM undertake a massive program to improve the quality of technical education for workers, managers and public officials. The goal of this program should be to increase the efficiency of the labor force by 10 per cent every year. Hence, the number of individuals in the labor force will remain constant. But the labor force measured in efficiency units will increase by 10 per cent every year.

a. Your recommendations were accepted and implemented. The efficiency of the labor force of the IRM is now increasing by 10 per cent per year. Calculate the following new "steady state" values for the IRM and explain your calculations:

1. Capital per worker

2. The Capital Stock

3. Real GDP per worker

4. Real GDP per capita

5. Real GDP

6. Saving per worker

7. Total saving

8. Gross Investment per worker

9. Depreciation per worker

10. Net Investment per worker

11. Gross Investment

12. Depreciation

13. Net Investment

14. Rate of growth of real GDP

15. Rate of growth of real GDP per worker

16. Rate of growth of real GDP per capita.

b. Construct a per-worker production function graph that illustrates the "steady state" values before and after the efficiency of the labor force of the IRM started to grow. (Label the axes and the curves and indicate the "steady state" levels of capital per worker, gross investment per worker and GDP per worker, before and after the efficiency of the labor force started to grow.)

c. Compare the current "steady state" capital stock per worker, investment per worker, consumption per worker and GDP per worker and Real GDP per capita with the "steady state" capital stock per worker, investment per worker, consumption per worker and GDP per worker after the efficiency of the labor force started to grow.

d. Compare the "steady state" growth rates of the following:

1. Capital stock per worker,

2. Real GDP per worker and

3. Real GDP per capita

4. Capital stock

5. Real GDP

with a constant efficiency of labor and with a growing efficiency of labor.

e. Compare the results of your proposal with that of the Chairman of the Council of Economic Advisors of the IRM. (1) Will efficiency growth increase the growth rate of the IRM? (2) Will efficiency growth increase or decrease the standard of living of the people of the IRM?

H. Endogenous Growth

a. How would your analysis of the IRM economy change if the Aggregate Production Function were as follows::

Y = K* L

a. Derive the per worker production function

b. Calculate the value of Real GDP per worker for the following possible levels of the capital stock per worker in the IRM:

c. Use the schedule you have prepared to graph the per- worker production function.

d. If this were the production function of the IRM, could you calculate the steady state amount of capital per worker? Explain your answer.

e. If this were the production function of the IRM,