Macroeconomics II
DS Questions
Question 1
Shocks to an economy, such as wars, famines, or the unification of two economies, often generate large
flows of workers across borders. What are the short-run and long-run effects on an economy of a onetime permanent increase in the stock of labor? Examine this question in the context of the Solow model
with g = 0 and n positive.
Question 2
Suppose the U.S. Congress decides to levy an income tax on both wage income and capital income.
Instead of receiving
wL + rK = Y,
(1)
consumers receive
(1 − t)wL + (1 − t)rK = (1 − t)Y,
(2)
where t is the tax rate. Trace the consequences of this tax for output per worker in the short and long
run, starting from the steady state.
Question 3
Suppose that there is a permanent increase in the rate of technological progress, so that g rises to g ′ .
Sketch a graph of the growth rate of output per worker over time. Be sure to pay close attention to the
transition dynamics.
Question 4
Consumption is equal to output minus investment: c = (1 - s)y. In the context of the Solow model
with no technological progress, what is the savings rate that maximizes steady-state consumption per
worker? What is the marginal product of capital in this steady state? Show this point in a Solow
diagram. Be sure to draw the production function on the diagram and show consumption, saving, and
a line indicating the marginal product of capital. Can we save too much?
Question 5
Consider a Solow economy with a production function:
Yt = Ktα (At Lt )1−α ,
where α ∈ (0, 1).
(3)
As in class, we consider an economy where productivity grows at a rate g (g > 0) and population grows
at a rate n (n > 0). Suppose the savings rate increases. Discuss its implications on:
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1. The growth rate of capital per unit of augmented labor,
2. The short and the long-run growth rate of output per capita,
3. The long-run levels of output per capita,
4. The short and the long-run growth rate of output,
5. The long-run levels of output.
Repeat the previous exercise when the depreciation rate decreases.
Question 6
Consider three scenarios:
• Scenario 1: n = 0, g = 0
[Think Greece]
• Scenario 2: n > 0, g = 0
[Think Mexico]
• Scenario 3: n = 0, g > 0
[Think Japan]
Now, answer the following:
1. Plot the growth rate of capital per unit of augmented labor against capital per unit of augmented
labor for each scenario. what happens to the long-run growth rate of output per capita in the
three scenarios.
2. Analyse what happens to the long-run growth rate of output in the three scenarios. which would
be the richest/poorest economy in terms of long-run levels of per-capita output.
3. Analyse which would be the richest/poorest economy in terms of long-run levels of GDP.
4. In which economy would you want to live? Give reasons.
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