The assignment is marked out of 25 points. The weight given to each part is indicated below. Style requirements: please keep THREE decimal places in your answers and include your EXCEL results as an appendix in your assignment. Please also take care to structure your answers clearly.

**Question 1**

Convergence in two sets of countries. Go to the website containing the Penn World Table and collect data on real GDP (expenditure-side real GDP at chained PPPs (in mil. 2011 USD)) and population from 1950 to 2017 for the United States, France, Belgium, Italy, Ethiopia, Kenya, Nigeria, and Uganda. Then you can construct real GDP per person for these countries. Define for each country for each year the ratio of its real GDP per person to that of the United States for that year (so that this ratio will be equal to 1 for the United States for all years.)

(1) Plot these ratios for France, Belgium, and Italy over the period for which you have data. Does your data support the notion of convergence among France, Belgium, and Italy with the United States? Give a brief explanation to rationalize your finding.

(2) Plot these ratios for Ethiopia, Kenya, Nigeria, and Uganda. Does this data support the notion of convergence among Ethiopia, Kenya, Nigeria, and Uganda with the United States? Give a brief explanation to rationalize your finding.

**Question 2**

Solow growth model. In this question, you will explore how changes in the saving rate and the rate of technological progress affect an economys growth. In addition, you will examine how the golden rule saving rate depends on the production function. Consider the Solow (neoclassical) growth model with aggregate production function Y = K?(AN)1 ?

. Each period lasts a year.

(1) Using the parameter values in Table 1, calculate the steady-state values of capital per effective worker k ? K/AN, output per effective worker y ? Y/AN and consumption per effective worker c ? C/AN. Calculate the golden rule saving rate. Also calculate the growth rates of output per worker and consumption per worker along the balanced growth path.

Intermediate macro: assignment #2 2

? 1/3 gA 3.0%

? 4% gN 1.0% s 16%

Table 1: Benchmark Parameter Values Solow model

(2) Suppose that the economy is initially in steady-state. In year t = 0 the saving rate increases from s = 0.16 to s = 0.25 (i.e., from 16% to 25%) while all other parameters have their benchmark values.

(i) Calculate the new steady-state levels of capital per effective worker, output per effective worker and consumption per effective worker. Does long-run consumption per effective worker increase? Also calculate the long run growth rates of output per worker and consumption per worker? Do the long-run growth rates of output per worker and consumption per worker increase? Explain.

(ii) Calculate and plot the time-paths of (a) capital per effective worker, output per effective worker and consumption per effective worker for 100 years (t = 0, 1,
., 100) and of (b) log output per worker and log consumption per worker. Describe and explain the short-run effect of the change in the saving rate on these variables.

Note: Here log means the natural logarithm, ln(·) = loge(·). To answer part (ii) of this question we need to know the level of productivity at year t = 0. Assume this initial level of productivity is A0 = 1. You will probably want to use a spreadsheet program to implement these calculations.

(3) We will now contrast these results with a change in the rate of technological progress. Suppose instead that at time t = 0, the rate of technological progress increases to 4% per year. With all other parameters as in Table 1 (in particular, with the saving rate s back at its benchmark value of 16%), calculate and plot the time-path of log output per worker for 100 years after the change in the rate of the technological progress (for t = 1, 2,
, 100), again assuming A0 = 1. Compare the time-path of log output per worker from the increase in the saving rate in part (2) to the time path with the increase in the rate of technological progress. How many years pass before output per worker surpasses the level that would be obtained from the increase in the saving rate? What does this suggest about the relative importance of level versus growth rate effects? Explain.

consumption per effective worker to derive how the steady state consumption per effective worker depends on the saving rate. With all other parameters as in Table 1, plot how the steady state consumption per effective worker depends on the saving rate for s = 0, 0.01, 0.02, 0.03,
, 1. In your plot, the horizontal axis should be the saving rate ranging from 0 to 1 and the vertical axis is the steady state consumption per effective worker. What is the golden rule saving rate?

**Question 3**

Endogenous growth model. You will explore the dynamics of human capital and physical capital using the human capital accumulation model. The aggregate production function is Y = AK?H1 ? . The values of parameters are shown as in Table 2. Each period lasts a year.

? 1/3 sK 20%

? 4% sH 15%

A 1

(1) Suppose an economy starts from K0 = 2 and H0 = 1. Calculate and plot the time paths of log human capital, log physical capital and log output for 100 years (t = 0, 1, 2,
, 100). Describe the dynamics of human capital and physical capital. What are the growth rates of human capital, physical capital and output in the long run? Has the ratio of human capital to physical capital converged to a steady state? If so, what is the steady state ratio of human capital to physical capital?

(2) Now suppose another economy starts from K0 = 1 and H0 = 2. Calculate and plot the time paths of log human capital, log physical capital and log output for 100 years (t = 0, 1, 2,
, 100). Describe the dynamics of human capital and physical capital. In comparison with your answers in part (1), how do the dynamics of human capital and physical capital change? What are the growth rates of human capital, physical capital and output in the long run? Has the ratio of human capital to physical capital converged to a steady state? If so, what is the steady state ratio of human capital to physical capital?

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