## 3 Questions

• November 30, 2020

(revised 9/24/2012 at 5:45pm – added question #5c.)

Economics Principles I                                                                                                                   New York University

Marc Lieberman                                                                                                Fall, 2012

Supplemental Problem Set #3

This problem set covers the use and construction of price indices. Recitations from Sept. 29– Oct. 3 will discuss some problems similar to these, especially problem 6, 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 were 1.2 in Dec. 2008, and 1.4 in Dec. 2009, what would the rate of inflation be for the year 2009?
3. If the price level were 1.4 in Dec. 2008, and the rate of inflation were 15% over the year 2009, what would the price level be in Dec. 2009?
4. If the price level were 1.3 in Dec. 2009, and the rate of inflation were 12% over the year 2009, what would the price level be in Dec. 2008?
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 questions 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.”  Which rule should you use?]
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. 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 wage rate over this one-year period. (That is, use the approximation method you presented in lecture )
• Using the data in problem 2, calculate the exact percentage change in the real wage over this one-year period.

(To get an exact percentage change, you can’t use the approximation method. You must first calculate and compare real wages in Aug 2007 and Aug 2008.  This requires you to 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.)

• Using the data of problem 2, suppose the hourly wage had been indexed to the official rate of inflation (as given by the CPI), starting in Aug 2007.  That is, from Aug 2007 to Aug 2008, assume the nominal wage had increased by the rate of inflation. What would the nominal wage have been in Aug 2008?  With indexation, what would have been the percentage change in the real wage between Aug 2007 and Aug 2008?
• Suppose you borrowed \$200 one year ago and must now repay \$210.  The inflation rate over the year was 7%.
1. What is the nominal interest rate on this loan?
2. Using the “approximation” method, what is the approximate real interest rate on the loan?
3. What is 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: For this problem, read the appendix to Ch. 7 (pp. 196-197). If you have difficulty understanding these pages, or how to use them to answer the questions below, attend one of the recitations this week.]

Suppose that an economy has only three goods, with prices and typical household quantities purchased at two times as shown below:

 GOODS Dec. 2012 Dec. 2013 Quantity per month Price per Unit Quantity per month Price per unit Pilates Lessons 5 \$20 3 \$30 Movies 5 \$18 8 \$15 Hamburgers 20 \$2 20 \$2.50
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 does 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 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) increase or decrease during 2013? By exactly what percentage?

[Hint: first calculate your own personal CPI, based on the good or goods that only you buy.  Since an exact number is requested, don’t use the approximation rule.]

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