1) Two economies, Hare and Tortoise, each start with a real GDP per person of $30000 in 2012. Real GDP per person grows 3% per year in Hare and 1% per year in Tortoise. In the year 2100, what will be real GDP per person each economy? First make a guess and then calculate the correct answer.
2) Over the past twenty years an economy’s total output has grown from $10000 to $13000, its capital stock has risen from $25000 to $32500, and its labor force has increased from 200 million to 230 million. All measurements are in real terms. Calculate the contributions to economic growth of growth in capital, labor, and productivity assuming
a) aK = 0.3 and aN = 0.7.
b) aK = 0.5 and aN = 0.5.
3) For Westeros, the following capital input K and labor input Nwere reported in four different years.
Year K N
1 200 1000
2 250 1000
3 250 1250
4 300 1200
The production function is Y = K0.3N0.7, where Y is total output.
a) Find total output, the capital-labor ratio, and output per worker in each year. Compute the growth rate of these three variables for each year. Can this production function be written in per-worker form? If so, determine the per-worker form.
b) Repeat (a) if Y = K0.3N0.8.
4) Consider the calibration of the Solow growth model, where population growth is
n = 0.01, depreciation is d = 0.04, the saving rate is s = 0.16, f(k) = Ak?,A = 554, and
? = 0.36.
a) Compute the steady-state quantity of capital per worker and output per worker.
b) Now suppose that A increases by 10%. Compute the new steady-state quantity of capital per worker and output per worker.
c) Did the capital to output ratio change? Explain your results.
5) Suppose that the economy is initially in a steady state, and some of the nation’s capital stock is destroyed because of a natural disaster or a war.
a) Determine the long-run effects of this on the quantity of capital per worker, and on output per worker.
b) In the short run, will aggregate output grow at a rate higher or lower than the growth rate of the labor force?
c) Consider the calibration of Problem 2. Suppose the per worker capital stock starts out at 90% of its steady state value. What will the capital-output ratio be then? What will the growth rate of capital from the first period to the second period be?
d) After World War II, growth in real GDP in Germany and Japan was very high. How do your results in the previous parts shed light on this historical experience?
6) An economy is in a steady state with no productivity change. Because of global warming, the rate of capital depreciation rises permanently.
a) According to the Solow model, what are the effects on steady-state capital per worker, output per worker, consumption per worker, and the long-run growth rate of the total capital stock?
b) In our endogenous growth model, what are the effects on the growth rates of output, capital, and consumption of an increase in the depreciation rate of capital?
7) Let us add a government to the Solow model. Suppose that the government purchases g goods per worker every year, so if there are Nt workers then Gt = gNt. The government has a balanced budget to its tax revenue Tt = Gt. Total national saving St = s(Yt?Tt), where s is the saving rate.
a) Graphically show the steady state for the initial level of government purchases per worker.
b) Suppose the government permanently increases g. What are the effects on the steady-state levels of capital per worker, output per worker, and consumption per worker? Does your result imply that the optimal level of government purchases is 0?