1. For each of the following statements, determine whether it is true or false and briefly explain your answer.
A1. As a result of technological progress, some products may become better and cheaper at the same time (consider the price and quality of computers 10 years ago). Our treatment of the value of goods in the calculation of GDP leads us to think that GDP growth may overstate economic growth in poor countries as they develop.
A2. By definition, the Gross National Product for any country will be larger than its Gross Domestic Product.
A3. People in richer countries tend to have higher educational attainment only because education increases people’s productivity.
A4. People in richer countries tend to have higher educational attainment only because rich people can afford more education.
2. Consider an economy described by the Solow growth model and the following production function. This is an example of a Cobb-Douglas production function; these are used very often in economics.
Y = F(K,L) = K1/3L2/3
a) Demonstrate that this production function exhibits constant returns to scale.
b) Write down the per-worker production function. Does the function exhibit diminishing marginal product of capital? Show this either with some numbers or a graph (or by taking the derivative if you are good at calculus).
c) Write down the per-worker capital accumulation equation for this economy. Assume that the growth rate of population is 5% and that there is no technological progress.
d) Suppose this country saves 20% of its income each year and that 5% of its capital stock depreciates each year. Assuming no population growth or technological progress, find the steady state level of capital per worker, output per worker and consumption per worker.
3. Two countries, Richland and Poorland are described by the Solow growth model. They have the same Cobb-Douglas production function Y=F(K,L) = K1/3(TL)2/3 . Note that this assumes that T is the same in both countries. Richland saves 32% of its income and Poorland saves 10% . Richland has population growth of 1% and Poorland has population growth of 3%. Both Economic Development Division of Social Science
Problem Set 1 HKUST
Due: March 13 canvas, only pdf file accepted
Page 2 of 2 countries have technological progress at a rate of 2% per year and a depreciation rate of 5% per year.
a) What is the per-effective-worker production function?
b) Write down the capital accumulation equation.
c) Write down the per-effective-worker capital accumulation equation.
d) What is the steady state level of output per effective worker in Richland?
e) What is the steady state level of output per effective worker in Poorland?
f) What is the steady state ratio of output per worker in Richland to Poorland?
g) If Richland actually produces 16 times the amount of output per worker than Poorland, how might you explain the income differential (hint: consider what factors can be important for economic growth but not included in the model; or consider whether the assumption on the rate of technical progress is held)?
4. Table 1-4 (see Excel workbook on Canvas) provides data on log(GDP per capita in 1990), log(GDP per capita in 2009), the average growth rate of GDP per capita between 1990 and 2009, investment as share of GDP, and the growth rate of population for 26 European countries.
a) Use Excel, plot the growth rate of GDP per capita against log(GDP per capita in 1990) for these 26 countries. Then plot the approximate line of best fit corresponding to the data (You may either print the graph and draw this line in the graph, or use the “trendline”
feature in Excel).
b) Is the approximate line that you get in part (a) slope upward or downward? How do you interpret this relationship? Is it consistent with the prediction of the Solow model?
c) Use Excel, plot the growth rate of population against log(GDP per capita in 2009) for these 26 countries. Then plot the approximate line of best fit corresponding to the data. Is the relationship shown in the plot consistent with the prediction of the Solow model?
d) Use Excel, plot investment as share of GDP against log(GDP per capita in 2009) for these 26 countries. Then plot the approximate line of best fit corresponding to the data. Is the relationship shown in the plot consistent with the prediction of the Solow model? For more information on GDP Comparison check out : https://www.encyclopedia.com/social-sciences-and-law/economics-business-and-labor/economics-terms-and-concepts/gross-domestic-product
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