Problem Set 1 (Economic Growth)
ECON 6002/6702/3902 - S2 2024
Marcel Peruffo
Due date: 8th of September
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NOTE: Please only include Student ID number (no name or unikey) on your submitted
answers. To receive full marks, show your workings for algebraic manipulations.
1. Suppose the aggregate production function in the Solow-Swan model is Cobb-Douglas, y = kα,
with α ∈ (0, 1).
(a) Derive k∗, y∗, and c∗ as functions of the model parameters and determine their values
when the saving rate is s.
(b) At some point in the previous derivation, you must have hadW (0) = [k(0)α−k(0)αk(0)α−1]
(with A(0) = 1)). Assume L(0) = 1. What does this formula (and the result from the
previous item) say about the labor share, i.e. the share of income in the economy that
corresponds to labor income?
(c) Find an expression for the the growth rate of wages w˙/w at any point in time.
(d) If the savings rate s suddenly changes to to s′ > s, at the moment of the change what
happens to capital? Why?
(e) Explain what the Golden Rule stands for. Why is it the case that when the savings rate
increase, consumption c∗ not always increase?
2. Now consider the Ramsey model as seen in class.
(a) From the steady-state expression for c˙c , derive the expression for the growth rate of per
capita consumption.
(b) Draw the transition dynamics if there is a decline in θ.
(c) What happens to the interest rate r∗ = f ′(k∗) given the decline in θ? Interpret.
3. The questions below refer to this Planet Money Podcast about the growth experiences of
the economies of China and Taiwan. To answer them, you must listen to it. The podcast
interviews Chang Tai Hsieh, one of the coauthors of the study about misallocation we had a
look at.
(a) Among the explanations we explored in class, which one fits best to the experience of
the Chinese farmers?
(b) What does the podcast suggest about the role of industrial policy in generating pros-
perity? It is a good or a bad policy? Or none?