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UC Berkeley, Economics 101B, Benjamin Schoefer, spring 2021. Do not share or circulate online or offline. Posted: 2/3/2021 Due date: deadline is Friday 13th, 5pm PST. Submission: submit a write-up of your answers via BCourses—either write up by hand on paper and then scan (or, rather than scanning, take a high-quality photo and compress to a reasonable file size while maintaining quality), or type up the problem set in Latex, Lyx, Scientific Wordplace, or any math/word processing software of your choice, and submit a PDF. Or, write up on a tablet and submit a PDF. Some resources for “mobile scanning” apps: https://www.nytimes.com/wirecutter/reviews/best-mobile-scanning-apps/ No matter the method, the file name of your submitted document must be “hw# FirstName LastName”, where # is homework number. For example, for this week, if your name were Janet Yellen, you would submit your homework one as “hw1 Janet Yellen”, without the ““” and “””, of course. Free tutoring services and problem set help: The Department offers free tutoring services to undergraduates taking 101B, e.g. for homework and exam preparation. Please take advantage of this terrific resource – the tutors are there (and paid by the department) to help you! Since our course will rely on math and resembles the structure of modern PhD macroeconomics courses, they will be particularly excited to talk about 101B problem sets, math questions and any other Ec101B topics. See their website for more information: https://www.econ.berkeley.edu/undergrad/home/tutoring You can work in groups of up to 4, but you must list the members of your group at the top of each problem set. Each student must write up and submit her/his own problem set, not simply copy consensus answers. Please review the code of conduct and definitions of cheating/plagiarism here: https://sa.berkeley.edu/conduct/facultystaff/violations ...and our honor code! https://teaching.berkeley.edu/berkeley-honor-code Late problem sets will be penalized by cutting the points in half per day. No exceptions. (No need to email us in advance or explain; just submit when ready.) We cannot devise extensions. See syllabus.

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GDP Deflator: basics 1. Fill in the “?” in the practice table for real/nominal GDP from lecture notes 1, slide 51. Show your math. 2. Why does real GDP (in 2018 and 2019 prices) not change between 2018 and 2019? 3. Why does real GDP change between 2019 and 2020, in 2019 prices? 4. Why do we obtain different numbers for real GDP growth depending on which year we use as the base year for prices? 5. Calculate the GDP deflator for each year, using 2018 as the base year. 6. How does the GDP deflator change, in percentage terms? Is this an inflation measure? Conceptually, how does this measure compare to changes in CPI inflation?

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GDP Deflator: application 1. Between 2006 and 2012, house prices fell by 40%. In 2006, residential construction was ca. 700 billion USD, and total GDP was ca. 13 trillion GDP, all at 2006 prices. By 2012, the housing bubble had burst, and house prices were 40% lower than in 2006, while prices of most other goods did not change a lot. By how much lower

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would real GDP be in 2006 if we instead used 2012 prices to value housing in 2006?1 Explain in words, but also show in (simple) math. 2. Suppose the 2006 market value of residential construction had been 1400 instead of 700 billion USD, driven by doubling the quantity of residential housing construction. How much would real GDP in 2006 now be different if we used 2012 house prices vs. 2006 house prices? 3. Is this an example for how real GDP measures and their growth are sensitive to which base year we pick for the prices? Optional reading on the housing bubble, its burst, and its aftermath (the Great Recession): https://en.wikipedia.org/wiki/United States housing bubble The House of Debt, Atif Mian, Amir Sufi, U. Chicago Press, 2015 Accompanying blog: http://houseofdebt.org/ Lawrence Summers on the crisis, and the book: https://www.ft.com/content/3ec604c0-ec96-11e3-896300144feabdc0 (or Google “Lawrence Summers on ?House of Debt?”) The video on the above FT website; interview with the authors. “The Big Short” – the book; the movie.

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Data exercise: growth of GDP For those of you unfamiliar with Excel, we will cover the basics necessary for this exercise in section.

The St. Louis Federal Reserve offers a terrific repository of macroeconomic data. Go to https://fred.stlouisfed.org/series/GDPC1 and download the time series. This is real GDP for the US, at the quarterly frequency, at 2012 dollars. Open the file in Excel or your preferred program. 1. Take the natural logarithm of the time series, which is done with the command ln(x) in a given cell. Plot the ln-transformed time series against the time variable. 2. Define growth in Excel, in the precise way: gtx =

xt − xt−1 xt−1

Plot this time series. 3. Compute the approximate growth we discussed in class and lecture, and plot this time series: gtx ≈ ln(xt ) − ln(xt−1 ) 4. How do these two time series of growth compare? 5. Download the GDP deflator time series, which takes 2012 as the base year, from: https://fred.stlouisfed.org/series/GDPDEF/ Add this time series to your Excel data set that contains real GDP. Note that the St. Louis Federal Reserve used exactly this deflator to compute the real GDP time series. Note also that in the base year, the GDP deflator is 100 rather than one. Therefore, divide all values for the GDP deflator by 100, to normalize it to 1 in 2012 (baseline year). Now back out nominal GDP for each quarter, using the GDP deflator. Plot the time series of nominal GDP in the same plot as real GDP. 6. What is the conceptual difference between nominal GDP and real GDP? 1 Suppose

that other prices have stayed perfectly constant (which is approximately true, given the low inflation during the Great Recession).

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GDP and its components 1. We discussed the following identity in class: Yt = Ct + Gt + It + N Xt Transform this identity into shares, by dividing by Yt . What is the interpretation of the expression? 2. Take the total derivative of the shares equation, with respect to the shares rather than the individual components, as we did in lecture. Why do the changes in the shares have to add up to zero? What is the interpretation of this fact? 3. Now take the difference between the original equation and its “lagged” counterpart: Yt−1 = Ct−1 + Gt−1 + It−1 + N Xt−1 You will find: Yt − Yt−1 = Ct − Ct−1 + Gt − Gt−1 + It − It−1 + N Xt − N Xt−1 Now additionally divide both sides of the difference by Yt−1 , and you will find (after some rearrangements on the right-hand side): Ct−1 Ct − Ct−1 Gt−1 Gt − Gt−1 It−1 It − It−1 N Xt−1 N Xt − N Xt−1 Yt − Yt−1 = + + + Yt−1 Yt−1 Yt−1 Ct−1 Yt−1 It−1 Gt−1 Yt−1 N Xt−1 Can you collect terms in this equation that represent growth of GDP components, and those terms that are shares? What is the interpretation? How does the growth of an individual GDP component affect or comove with GDP growth over time?2 4. Review lecture 1. Which component of GDP did that lecture show to constitute the largest share of GDP? 5. Given that fact, let’s understand how changes in this component (the largest share of GDP, which you just named) should affect GDP. How would a 10% fall (i.e. a growth of minus 0.1) in this variable affect GDP growth, assuming that all other components stay constant? 6. Now compare the GDP effect of this component to the analogous GDP effect of another – smaller – component of GDP: government expenditure. If G falls by 10%, what impact on GDP would this drop in G have, holding all other components constant? 7. By how much would G have to increase in order to offset a 10% drop in C, that is, in order to leave GDP growth unaffected by the consumption drop? 8. By how much would G need to increase to similarly offset a 10% fall in I (rather than C )? 9. As macroeconomists, (why) should these findings motivate us to study and model C first, rather than one of the other GDP components?

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Consumer theory in the real world

Briefly describe three real-world examples of substitution effects, namely consumers’ purchase/consumption decisions in response to changes in relative prices.3 [Two sentences per example.] You can make up abstract situations, or refer to actual (historical, current or anecdotal) events. Example: “The price of gas increased in the late 1970s. As a result, consumers switched from fuel-inefficient vehicles to fuel-efficient vehicles.” 2 To 3 Do

simplify things, you can suppose that shares are very stable (don’t move). not repeat examples discussed in lecture/section.

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Consumer theory exercises 1. Solve the following exercises from the textbook, at the end of chapter 1, pages 12, 13: 1.1 Sales tax 1.2 Indifference maps 1.3 An important utility function 2. What consumption value c maximizes the following utility functions respectively (each only consisting of one argument): U (c) = αc

(1)

U (c) = αln(c)

(2)

U (c) = γ − (c − c¯)2

(3)

U (c) = −β(c − c¯)2

(4) 2

U (c) = αc − β(c − c¯)

(5)

3. In general, what is a utility function? 4. By solving for the c (or any other choice variable of the consumer) that maximizes the utility function, do we make a prediction about how the consumer likely behaves in reality? 5. Now consider a consumer that faces a choice between 2 consumption goods on a budget, so the household faces a budget constraint and a trade-off, with the following utility function: U (c1 , c2 ) = α + u(c1 ) + βu(c2 ) s.t. c1 p1 + c2 p2 = Y where u′ > 0, u′′ < 0. Go to the optimality condition, by which M RS equals the price ratio. That expression will define the relative consumption of the two goods. What is the interpretation of the MRS? 6. What is the role of α? 7. What is the role of β here? How does the consumer change her allocation of consumption between good 1 and 2 if β falls? In terms of relative consumption, how does a lower β compare to a change in the relative prices between the two goods? To answer these questions, again go to the optimality condition by which the MRS equals the price ratio. 8. In the previous example, now assume a specific functional form for u(ci ) = ln(ci ), so that U (c1 , c2 ) = α + ln(c1 ) + βln(c2 ). Solve for the relative consumption explicitly, going from the “MRS equals price ratio” optimality condition. How does β show up? 9. Suppose that all consumers have the same utility function using the natural log specification, except that β varies between consumers. There are only two goods, and everyone faces the same prices, and has the same budget. How would you measure β in the data? Preview: A parameter resembling β will turn out to be a crucial parameter for our investigation of intertemporal consumption decisions.

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