Intermediate macroeconomics
Question 1- Solow Model with a Fixed Factor
Consider the Solow growth model (savings rate is exogenous) with the following aggregate production function
;
where Z is land. The supply of land is fixed. Assume that < 1, capital depreciates at rate d, and there is an exogenous savings rate of s.
1. Suppose there is no population growth rate. Find the steady state capital-labor ratio and the steady-state output per worker. Interpret the expressions.
2. Now suppose population grows at rate gN. What happens to steady state capital-labor ratio and output per worker? What does this imply when gN becomes a very large number? Interpret the expressions.
Question 2 – Growth Accounting –India
In this exercise you will carry out growth accounting for India for the period 1980-2003. The data is provided below.
The variables (from the first column to the last one) are as follows: 1.t- Year 2.
Y – Aggregate Real GDP, 3. K-Aggregate Capital Stock, 4. N:-Aggregate Employment
Suppose the production function for the aggregate economy is given by
;
where A is the Solow residual. Assume a = 1/3.
a. Use the data on aggregate GDP (Y), aggregate capital (K) and aggregate employment (N) to generate the Solow residual. Then, compute the contribution of growth, from 1980 to 2003, in aggregate capital, aggregate employment and in Solow residual to account for the growth in aggregate GDP. What is the source of growth in India’s GDP?
b. Take the production function in the first part and redo the growth accounting exercise with a = 0.44. Compare your results with those in part 1, and interpret the change in results.
Year Y K N
1980 372373 905948.7 2.2E+08
1981 401128 944265.3 2.26E+08
1982 425072 988245 2.33E+08
1983 438079 1050137 2.4E+08
1984 471742 1101336 2.46E+08
1985 492077 1147762 2.53E+08
1986 513990 1208254 2.61E+08
1987 536257 1276005 2.72E+08
1988 556778 1343211 2.79E+08
1989 615098 1394053 2.86E+08
1990 656332 1468858 2.93E+08
1991 692871 1545813 3.01E+08
1992 701863 1625952 3.08E+08
1993 737791 1718182 3.16E+08
1994 781345 1799651 3.19E+08
1995 838031 1892475 3.22E+08
1996 899563 2014541 3.25E+08
1997 970083 2176816 3.29E+08
1998 1016594 2327369 3.33E+08
1999 1082747 2457023 3.37E+08
2000 1148367 2579242 3.4E+08
2001 1198592 2691990 3.43E+08
2002 1267945 2805577 3.47E+08
2003 1318362 2915393 3.54E+08
Question 3- Solow growth model
a. Graphically illustrate and explain the effects of an increase in the rate of depreciation (d) on the Solow growth model. In your graph, clearly label all curves and equilibria.
b. Suppose policy makers wish to increase steady state consumption per worker. Explain what must happen to the saving rate to achieve this objective.
Question 4- Solow growth model
Graphically illustrate and explain the effects of a reduction in the saving rate on the Solow growth model. In your answer, you must clearly label all curves and the initial and final equilibria. In your answer, explain what happens to the rate of growth of output per worker and the rate of growth of output as the economy adjusts to this decrease in the saving rate.
Question 5- Technological Progress: The Short, the Medium, and the Long Run
Using the AS/AD model, graphically illustrate and explain the short-run and medium-run effects of a reduction in productivity. In your graph, clearly label all curves and equilibria. For simplicity, assume that the change in productivity has no effect on aggregate demand.