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# Economics 304 Homework #1 – A ride into reality

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Instructions: Please show all work or points will be taken off. Good luck!

1. (60 points total – 10 points each part) In this first homework assignment, we are getting our ‘hands dirty’ to get familiar with some of the major macroeconomic variables that we will be using and working with throughout the semester. Our first chapter with ‘something to sink our teeth into’ is chapter 3 and it is all about the factors of production, the labor market, and of course, the production function. Major variables in this part of the macroeconomy (i.e., the supply side of the economy) include, but certainly are not limited to, employment (denoted N), real wages (denoted w = W/P where W = nominal wage and P is the price index - typically the CPI) and real GDP (denoted Y). When we move to chapter 4 we encounter many more major macroeconomic variables including consumption (C), investment (I), and the real interest rate (denoted r), among others. We are going to use FRED as our source of data (many professional economists use this site, nice clean data!)

I provide you with the links to the data that is needed throughout this assignment. For an interesting look at the %ΔW vs. the %ΔP, click Here.

Use the following two links to answer the following questions:

For Nominal Wages (W) Click Here

Price index CPI (P) Click Here

I recall back in the early 1990s (before many of you were born!) when Bill Clinton was running for President and he was arguing that under the Bush Sr. Administration (1989-1992) that real wages for Americans actually fell implying that on average, workers were better off (in terms of the real wage) at the beginning of the Bush Administration compared to the end of the Bush Administration.

a) Calculate the real wage (W/P) the first month of the Bush Sr. Administration (1/89) and compare it to the last month of the Bush Sr. Administration (12/92). Please show all work. Was Bill Clinton correct in his claim? Why or why not?

b) The last four years of the Clinton Administration were arguably the absolute best in terms of the recent performance of the US economy (1/97 - 12/00). When we get to Chapter 3, we will discuss this period in much more detail and we refer to this period as the "new economy." Of course one metric of the health of any economy is the behavior of the real wage. In this part, we repeat the analysis above but use the final four years of the Clinton Administration. In particular, calculate the real wage (W/P) the first month of Clinton's second term (1/97) and compare it to the last month of Clinton's second term(12/00). Did real wages rise or fall during this period? Please show all work.

c) Now do the same with the Obama Administration. That is, calculate the real wage at the begining of the Obama Aministration (1/2009) and compare it to the present real wage (use the most recent available data).

d) When I used to fish in Miami, say June of 2001, I used to tip the captain and mate $30. Calculate the tip that I would need to give the captain and mate 1) 10 years prior (June of 1991) and 10 years hence (June of 2011) that would have the same purchasing power as my tip in June 2001. In other words, calculate the tips that I would need to give the captain and mate so that they can achieve the same level as satisfaction as in June 2001 (assume importantly that the basket they consume is same as the CPI basket).

e) Using the most recent data, calculate the percent change in the real wage over the most recent 12 months in two different ways. First, calculate the real wage one year ago and now and take the percent change of those two numbers. Second, use the approximation as we used in class...%Δ(W/P) = %ΔW - %ΔP. That is, take the percent change in nominal wages and subtract the percent change in prices (aka inflation). Now compare your two answers, is the approximation close to the real deal?

To answer f) you need to use the following link:

Employment (N) Click Here

f) Draw a graph with the real wage (w=W/P) on the vertical axis and employment (N) on the horizontal axis. Locate the initial conditions (calculate the real wage when you were born as well as the number employed) as point A and the conditions as of the present as point B. Use actual numbers and label your points accordingly. Your graph should have two points and no lines. How many more people are working now relative to when you were born (hint, the answer is in millions)?

2. (70 POINTS total - 10 points each part) Another critically important real economic variable we consider in this homework assignment is the real interest rate. We learned that the real interest rate is the difference between nominal interest rates and inflation. In fact, there are two real interest rates: ex-ante and ex-post. Ex-ante real interest rates are the expected real rates where ex-post real interest rates are the real rates that were actually realized. An example will help. Suppose one year nominal interest rates are 5% and you expect that prices are going to rise by 3% (i.e., your expected rate of inflation (πe) is 3%) over the holding period = one year. Your ex-ante or expected real rate of interest is therefore 2%. Now suppose that over the year inflation wasn’t 3% but 4% instead (your expectation rate of inflation was wrong). That is, actual inflation (π) equaled 4% and thus your actual real rate, referred to as the ex-post real rate of interest is only 1%. Naturally, ex-ante and ex-post real interest rates differ anytime expectations of inflation are different than the actual rate of inflation. To summarize, the ex-ante real rate is equal to i – πe where the ex-post real rate is equal to i – π. In general, it is the ex-ante rate that is most important since we base decisions today, in part, on expectations of the future (decision making under uncertainty!!!!).

In this problem. we are going to calculate real interest rates, both ex-post and ex-ante. The data you need for this problem are given below:

Nominal one year rates (i) Click Here

Price index CPI (P) Click Here

Expected Inflation Click Here

A couple notes are in order.

i) Expected inflation data is one year hence - so for example, expected inflation for the period from July 2010 to July 2011 is given in July 2010 and if you view the data, the expected inflation during this time is 2.7% = πe.

ii) To calculate the actual rate of inflation, for example, during the July 2010 to July 2011 period you need to take the percent change in P = %Δ P. Using the CPI data, we have the

price index equaling 217.6 in 7/2010 (beginning of August given the end of month data) and 225.4 in 7/2011 (end of July, 2011). Note, this is a 12 month period. The actual rate of inflation during this time is 3.58% = π

iii) When using the one year nominal interest rate to calculate the all important real rate(s) of interest we need to be careful. For example, using the same one year time period (July 2010 - July 2011) we simply use the one year rate given as of July 2010. Think of buying the bond in July 2010, putting it in a safety deposit box (or under your mattress, a coffee can, etc.) and then cashing it in when it matures in July 2011 (you get your principal times whatever the nominal interest rate is). In viewing the data, the one year rate in July 2010 is 0.29%. So clearly (and by design of the Fed), both the ex-ante and ex-post real rates are negative during this period and differ because expected inflation was not equal to actual inflation.

2 a) Calculate the ex-ante and ex-post real rate of interest between July 2008 and July 2009. Why are these real rates so different? Again, please show all work.

b) We know that most decisions are in part, based on expectations of the future. Suppose we have two people who are trying to decide whether to consume today (August 2008) or save for the future and consume one year later, in August 2009. One person, let's call him Joe, is basing their decision on the ex-ante real rate of interest like most of us do. The other person who has a crystal ball, we'll call her Crystal, can see exactly what the actual rate of inflation is going to be and thus, has perfect foresight and bases their decision on the ex-post real rate. Given the difference in the ex-ante and ex-post real rates above, who would be more likely to save and who would be more likely to spend? Explain in detail and feel free to use the shopping cart example we used in class.

c) Given the most recent data, what is the ex-ante one year real rate of interest? Is this higher or lower than the ex-post real rate of interest or don't we know? Explain.

We discussed the evils of deflation.

d) From a macroeconomic perspective, why is deflation so bad? Please refer to consumer behavior and the corresponding behavior of firms in a deflationary environment.

e) Now discuss the fact that deflation is the central bank's worst nightmare. Make sure you refer to either the ex-post or ex-ante real rate that you calculated above, whichever applies. Why is this environment such a nightmare for the central bank and monetary policy? Explain using the Fisher equation for the real rate of interest.

f) Suppose Joe, from part b) above, changes his expectation of inflation to equal the actual rate of inflation that occurred between July 2008 and July 2009. What is the lowest the ex-ante interest rate can go, given the change in Joe's inflationary expectations. Click Here for a hint!

g) Given a deflationary environment, what can the central bank do to rid themselves of the nightmare? Explain. Click Here for a hint! Explain why this move is supposed to work in terms getting rid of the nightmare.

3. (50 points total – 10 points each part) Real vs nominal GDP. When we get to chapter three we consider a production function where the output of all our factors of production is of course real GDP. Recall that Nominal GDP is the total value of goods and services produced at current prices where real GDP is the total value of goods and services expressed in constant prices (we deflate nominal GDP by a price index called the GDP deflator). The links for the data used in this problem are below.

Nominal GDP GDP

GDP Deflator (P) GDPCTPI

a) Let us examine the so-called "Great Recession" that occurred from December 2007 (fourth quarter since data on GDP and the GDP deflator are quarterly) to June 2009 (second quarter). Click here for the NBER site. Calculate the percent change in real GDP by calculating real GDP at the beginning of the recession as well as calculating real GDP at the end of the recession and then, take the percent change. Please show all work. (for all calculations use the data from 2007-10-01 to 2009-04-01.)

b) Let us go back to the 1973 – 1975 recession. Note that officially, this recession began in fourth quarter of 1973 and ended in the first quarter of 1975. Calculate the percent change in real GDP in the same manner as you did above in point a) (for all calculations use the data from 1973-10-01 to 1975-01-01 (GDP data is quarterly).

c) Now calculate the percent change in the GDP price deflator (P) during this 1973 - 1975 recession.

d) What is this period often referred to and why (starts with S!)?

e) Finally, draw a graph with the general price level on the vertical axis (the GDP deflator) and real GDP on the horizontal axis. Label the initial point (the beginning of recession) as point A and the end point (the end of recession) as point B. Be sure to label graph completely using the specific numbers you calculated above.

## [Solved] Economics 304 Homework #1 – A ride into reality

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- ExpertT
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The Nominal wage (W) at the first month of the Bush Sr. Administration (1/89) was $9.65 and the price index(P) was 121.600 thus the real wage was = W/P = ...