## Problem Set 3.doc

• December 3, 2020

Revised 9/29/2014: This version corrects a minor typo in the instructions (corrected in red)

Introduction to Macroeconomics                                                                                        New York University

Marc Lieberman                                                                                                Fall, 2014

Supplemental Problem Set #3

Do the problem set by the suggested “due date” posted in the Aplia course outline.  Some of the questions also appear as part of the Aplia problem set, but don’t ignore the other questions on this problem set – they are all important. Answers will be posted in the “Course Materials” section shortly after the due date.

Recitations on Sept. 26 and Sept 29 will discuss some problems similar to these, especially problem 6 5 which covers how the CPI is constructed from actual data. The construction of the CPI is also discussed in the Appendix to Chapter 7 in your textbook.

1. Answer each of the following questions:
2. If the price level was 1.2 in Dec. 2012, and 1.4 in Dec. 2013, what was the rate of inflation for the year 2013?
3. If the price level was 1.4 in Dec. 2012, and the rate of inflation was 15% over the year 2013, what would the price level be in Dec. 2013?
4. [Read carefully] If the price level was 1.3 in Dec. 2013, and the rate of inflation was 12% over the year 2013, what was the price level in Dec. 2012?
5. If the average nominal wage rises from \$10 to \$12 over some time period, and price level rises from 1.0 to 1.1 over the period, what is the exact (not approximate) percentage change in the real wage over the period? [Hint: Do not use the approximation rule, because this question asks for the exact percentage change.]
6. If the average nominal wage rises from \$10 to \$12 over some time period, and price level rises from 1.0 to 1.1 over the period, what is the approximate percentage change in the real wage over the period? [Hint: use the approximation rule for percentage changes in real variables presented in class—“rule #3.”]
7. If the average real wage rises from \$10 to \$10.50 over some period, and the price level rises from 1.0 to 1.1, what is the approximate percentage change in the average nominal wage? [Hint: Notice the word “approximate.”  So, you’ll be using a version of the approximation rule here.]
8. Suppose that, over a time period lasting 3 years, the nominal wage rises by 5% per year.  Over the same time period, the annual rate of inflation is 3%.  What is the exact total percentage increase in the real wage over this entire time period? [Hint: This question asks for the exact percentage change. So…which rule should you use?]
• [Note: This problem uses actual data from the Bureau of Labor Statistics] In Aug 2007, U.S. private‑sector workers earned an average of \$17.42 per hour.  In August 2008, this figure had increased to \$18.05  Over the same period, consumer prices increased by 5.4% (according to the CPI).  Using these numbers, find the approximate percentage change in the real hourly wage rate over this one-year period.

[Hint: use the approximation method you learned about in lecture  To do this, you’ll have to first figure out the % change in the nominal wage.]

• Using the same data in problem 2, now calculate the exact percentage change in the real hourly wage over this one-year period.

[Hints: To get an exact percentage change, you can’t use the approximation method. You must calculate the real wage in Aug 2007 and the real wage in Aug 2008, and then figure out the percentage change.   In order to calculate these real wages, you must first construct a price index to reflect the rise in the price level over that one-year period.  The easiest way to do this is to use Aug 2007 as your “base period”, and arbitrarily set your price index equal to 1.0 for that month.  Then, based on the inflation rate given in the problem, calculate the value your price index must have in Aug 2008. Use those price indices to calculate and compare real wages.]

• Suppose you borrowed \$200 one year ago and must now repay \$210.  The inflation rate over the year was 7%.
1. Based on how much you borrowed and how much you paid back, what was the nominal interest rate on this loan?
2. Using the “approximation” method, what was the approximate real interest rate on the loan?
3. What was the exact real interest rate on the loan? [Hint: Do not use the approximation method this time.  Instead, construct a price index for the beginning and end of the year, calculate the purchasing power of the amount borrowed with the purchasing power of the amount paid back, and calculate the percentage difference in those two amounts.]
• [Note: To learn how to do this problem, you can either (1) read the appendix to Ch. 7 (“Calculating the Consumer Price Index”); or (2) attend one of the recitations this week.  Or both.]

Suppose that an economy has only three goods, with prices and typical household quantities purchased in two different time periods as shown below:

1. Using Dec. 2012 as a base period, calculate the CPI for Dec 2012 and for Dec 2013, as it would be determined by the BLS.
• Based on this data, what will be the officially reported inflation rate for the year 2013?
• When the BLS makes its official CPI calculations, how many Pilates Lessons would it assume the typical family buys in Dec 2013? [Hint: what does the BLS assume about quantities?]  In this economy, does the BLS’s assumption cause it to overstate or understate the rise in the “cost of living” during 2013?  Briefly, explain why.
• Suppose you only buy movies (you don’t like Pilates, and you grow all of your own food so you don’t need to buy hamburgers.) Suppose also that, between Dec. 2012 and Dec. 2013, your nominal wage is indexed to the official rate of inflation for the economy.  Would your real wage (i.e., the purchasing power of your own personal wage based on what you actually buy) increase or decrease during 2013? More specifically, what would be the exact percentage change in your own, personal real wage?

[Hint: The easiest way to answer is to pick an arbitrary nominal wage (say, \$10) for Dec 2012.  Based on your choice, and the info in the question, what will your nominal wage be in Dec 2013?  Then, to figure out what happens to your real wage, calculate your own personal CPI, based only on the good or goods that you buy. And note that the question asks for an exact percentage change, so don’t use the approximation rule for this one.]

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