Problem Set 1 (Economic Growth) ECON 6002/6702/3902 - S2 2024 Marcel Peruffo Due date: 8th of September ————————————————————————————————————- 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? 51作业君版权所有