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Intermediate Macroeconomics
Second Midterm
Juan Rubio-Ram´ırez
Fall 2020
Please write the answers in the space provided and show all your work. During the exam, you
may use a calculator; use of hand-held electronic devices (such as cell phones, for instance) during
the exam is strictly prohibited. This is a closed-book exam. You must remain in the room when
you write your examination. You may not refer to any books, notes, or other material.
Look over the entire exam before you start. Please be as concise as possible when writing your
answers. Whenever possible, use simple math or diagrams to help make your point more clearly.
Be careful to answer each of the question(s) asked (and nothing more) in a way that communicates
clearly your understanding of the issue(s) addressed in the question. There is a total of 100 points.
Good luck!
1. (25 points) Consider a standard Solow model. The production function is given by Yt=
AtKα
tN1−α
t, with saving rate s, depreciation rate δ, population growth at rate nand technol-
ogy A.
(a) (5 points) Calculate the steady-state value for per-capital capital in the model.
(b) (5 points) Assume that at time “t” the population growth increases permanently from
“δ” to “˜
δ”, where ˜
δ > δ. Calculate the new steady-state value for per-capital capital.
(c) (2 points) Is it bigger or smaller?
(d) (5 points) Show in a time-diagram the evolution of per-capita capital, aggregate capital,
and population before and after the population growth increased.
(e) (5 points) Show in a time-diagram the evolution of per-capita output and aggregate
