|Review of the Solow model. Suppose that the production function is given by Y(t) = AK(t)“L(t)l-«, where A is a fixed technological parameter. There is no technical progress over time. Assume a fix rate of depreciation 8, a fixed savings rate s, and a constant rate of growth of population n. a. Write down the equation that describes the accumulation of capital stock over time in terms of per capita capital stock k(t) and per capita income y(t).
|Review of the Solow model. Suppose that the production function is given by Y(t) = AK(t)“L(t)l-«, where A is a fixed technological parameter. There is no technical progress over time. Assume a fix rate of depreciation 8, a fixed savings rate s, and a constant rate of growth of population n. a. Write down the equation that describes the accumulation of capital stock over time in terms of per capita capital stock k(t) and per capita income y(t).
Chapter1: Making Economics Decisions
Section: Chapter Questions
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Transcribed Image Text:Review of the Solow model. Suppose that the production function is given by Y(t) =
AK(t)ª L(t)'-«, where A is a fixed technological parameter. There is no technical progress
over time. Assume a fix rate of depreciation 8, a fixed savings rate s, and a constant rate
of growth of population n.
a. Write down the equation that describes the accumulation of capital stock over time in
terms of per capita capital stock k(t) and per capita income y(t).
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b. Given your answer to part a., use graph(s) to explain why there exists a steady state in
the Solow model.
c. Recall that the Harrod-Domar has the following production function Y = K. Given
your answer to part a., use graphs to explain why there does not exist a steady state in
the H-D model.
d. Now let us go back to the Solow model. Recall that in the steady state, k(t) =
k(t + 1) = k*. Given your answer to part a., explicitly solve for the steady state value
of the per capita capital stock k* and per capita income y* (i.e., solve for k* and y* as
functions of the exogenous parameters).
e. Discuss how k* and y* change in response to a rise in (1) the technological parameter
A, (2) the rate of savings s, (3) a, (4) the depreciation rate 8, and (5) the population
growth rate n.
f. What is the rate of growth of k* and y* in the steady state? What about K(t) and Y (t)?
g. This question involves no technical progress. Will you be able to answer similar
questions if we assume a non-zero rate of technical progress, t? (No need to answer
this question. Just something you may want to consider while preparing for the exam.)
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