1 Exploring Data
Go to the Angus Maddison project (https://www.ggdc.net/maddison/maddison-project/data.htm), which computes real GDP per capita for several countries, dating back, in some cases, to the first century. This information can be downloaded from the website and it is expressed in 1990 Geary-Khamis dollars. Use these data to answer the following questions.
1. Do a web search and briefly explain what Geary-Khamis dollars mean.
2. Plot GDP per capita in one graph for the United States, China, and India from 1929.
3. Compute the average growth rate of the United States, China, and India between 1990 and 2010. Detail the steps you take and discuss your results.
4. Assume that GDP per capita in all three countries will continue to grow at the average growth rates they have experienced during 1990-2010. Starting from 2010, how long will it take for India and China to catch up with the US in terms of GDP per capita? Detail the steps you take and discuss your results.
5. Plot your estimated GDP per capita for India and China, relative to the US, from 2010 to 2050, i.e., GDPChina or India/GDPUS.
6. Choose three countries you are particularly interested in and describe their growth experiences relative to the US in the last century. Describe anything interesting you may want to highlight, for example the effect of wars or other events on the growth in those countries.
2 The Solow Growth Model
In a version of the Solow growth model: (1) The aggregate production function is Y = AKaHb, where A is the technology level, K is the capital stock, and H is the total efficiency units of labor; (2) The depreciation rate of capital is d ∈ (0, 1); (3) The saving rate of households is s ∈ (0, 1). A, H, d and s are parameters.
1. Write the investment at time t, It, as a function of capital stock at time t, Kt.
2. Write the capital stock at time t + 1, Kt+1, as a function of capital stock at time t, Kt.
3. Define the steady-state equilibrium in this economy and derive the equation that pins down the steady state level of capital stock, K∗.
4. For each of the three cases below, draw the aggregate production function with respect to K (just the shape of the function) and discuss whether it satisfies the law of diminishing marginal product.
(a) a > 1;
(b) a = 1;
(c) 0 < a < 1.
5. Let a = 0.5, b = 1, A = 1, H = 1, d = 0.1, s = 0.2. Solve for the steady-state levels of capital stock K∗, output Y∗, and investment I∗.
6. Let a = 0.5, in a graph with K on the x-axis:
(a) Draw the total savings as a function of K;
(b) Draw the total depreciation as a function of K;
(c) Find the the steady-state equilibrium in the graph.
7. Using the graph from the last question, discuss what will happen over time if the economy starts with a capital stock K0 that is lower than the steady-state capital stock level, K. What if K0 is greater than K?
8. Suppose the economy is at the steady-state equilibrium. Using a graph to discuss and illustrate the effects of a technology progress to the economy.
3 Employment and Unemployment
1. Suppose that the unemployment rate is 5%, the number of potential workers is 100 million, and the number of unemployed workers is 2.5 million.
(a) Compute the labor force;
(b) Compute the number of employed workers;
(c) Compute the labor force participation rate.
2. Discuss the effects of a minimum wage law to the labor market using the supply-and-demand framework (Hint: You should discuss separately based on whether the minimum wage is higher or lower than the market clearing wage)