# Intermediate Macroeconomics – Problem Set 2

Document Type
Essay
Pages
3 pages
Word Count
2023 words
Intermediate Macroeconomics
Juan Rubio-Ram´ırez
Fall 2020
Problem Set 2
Due Date: By the end of the day (11:30 PM), March 2nd
Instructions: You may work on this problem set in groups of up to three people; should you choose to do so,
please make sure to legibly write each group member’s name on the first page of your solutions. Also: i) be neat,
ii), for the data part, if the question asks for a graph, copy the graph from Excel to Word and write your answer
next to or below it, iii)when graphing, label all plots, series, and axes accordingly, iv)if a graph has a time
dimension, always plot it on the horizontal axis, v)write down your name, vi)staple all pages together. Have
fun!
Production Function
1. Williamson, 5th edition, problem 2.12 (slightly modified). You need to do this problem in Excel.
Let Ktdenote the quantity of capital a country has at the beginning of period t. Also, suppose that capital
depreciates at a constant rate δ, so that δKtof the capital stock wears out during period t. If investment
during period tis denoted by It, and the country does not trade with the rest of the world, then we can say
that the quantity of capital at the beginning of period t+1 is given by
Kt+1=(1δ)Kt+It.
This equation is often referred to as the “law of motion for capital.” Suppose at the beginning of year 0 that
this country has 80 units of capital. Investment expenditures are 10 units in each of years 0,1,2,3,4,...,10.
The capital stock depreciates by 10% per year.
(a) Calculate the quantity of capital at the beginning of years 0,1,2,3,4,...,10.
(b) Repeat 1a, except assume now the country begins year 0 with 100 units of capital. Explain what

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