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Economics 101: Winter 2017 UC Davis Sketch Solutions February 28, 2017 PART A: Multiple Choice Questions Each question is worth 3 marks (30 marks in total). MARK YOUR ANSWERS ON YOUR SCANTRON FORM 1. For the years 1948–1973, output per person in the private sector grew 3.3 percent. The growth contribution from labor composition was 0.2 percent, and total factor productivity grew by 2.2 percent. What was the growth contribution from capital per person? (a) 1.5 percent (b) 1.3 percent (c) 3.2 percent (d) 5.3 percent (e) 0.9 percent Answer: (e). The growth accounting decomposition is: growth in output per person = the contribution from capital per person + contribution of labor composition + TFP growth. The answer is therefore: 3 . 3 - 2 . 2 - 0 . 2 = 0 . 9 2. In the Romer model, if an economy’s research share decreases, there will be: (a) an immediate decrease in output and output growth slows (b) an immediate increase in output but output growth slows (c) an immediate increase in output and output growth accelerates (d) an immediate decrease in output but output growth accelerates (e) no change in output but output growth slows. Answer: (b). The fall in the research share means more people to work in final output production. Initially output goes up, but fewer researchers eventually means less innovation and lower growth. 3. Consider the following table and answer this question using the bathtub model of unemployment. Recall that in the bathtub model, U ⇤ = ¯ s ¯ L ¯ s + ¯ f . Separation rate Finding rate Labor force 2015 2% 20% 130 2016 2.5% 15% 100 In 2015 the natural rate of unemployment is: 1 This study source was downloaded by 100000881534062 from CourseHero.com on 05-19-2024 19:11:29 GMT -05:00 https://www.coursehero.com/file/193350263/MT22017SketchSolutionspdf/

(a) 11.8 (b) 0.2 percent (c) 10.0 percent (d) 90.9 percent (e) 9.1 percent Answer: (e). u ⇤ = U ⇤ / ¯ L = (2 / (2 + 20)) = 0 . 091 4. Suppose a college student earns $70,000 per year after graduating and works for 45 years. The interest rate is 2%. What is the present discounted value of their life-time earnings (assuming no growth in wages)? (a) $0.1 million (b) $0.4 million (c) $2.1 million (d) $1.8 million (e) $23 million Answer: (c). PDV = w ⇥ (1 - ( 1 1+ R ) T ) (1 - ( 1 1+ R )) = 70000 ⇥ (1 - ( 1 1 . 02 ) 45 ) (1 - ( 1 1 . 02 )) = $2 . 1 million 5. In 2007, the movie Transformers generated about $27.8 million on its opening day. In 1995, Batman Forever generated $20 million on its opening day. The CPI in 2005 was 100, the CPI in 1995 was 78.0, and the CPI in 2007 was 106.2. Which is the larger single-day grossing movie in 2005 dollars? And what was the revenue of this movie in 2005 dollars. (a) Transformers; $27.8 million (b) Transformers; $35.6 million (c) Batman Forever; $35.6 million (d) Batman Forever; $27.8 million (e) Transformers; $26.2 million Answer: (e). Transformers: 27 . 8 / 106 . 2 ⇥ 100 = 26 . 18. Batman: 20 / 78 . 0 ⇥ 100 = 25 . 64. 6. You are the head of the central bank and you want to maintain 2 percent long-run inflation. You use the quantity theory of money. If the real GDP growth is 4 percent and velocity is constant, you suggest a: (a) 6 percent interest rate (b) 6 percent money supply growth (c) 2 percent money supply growth (d) 0 percent money supply growth (e) 2 percent interest rate Answer: (b). From the quantity theory in growth rates: ⇡ = g m - g y (with constant velocity). 2 = g m - 4 implies g m = 6. 7. During the Great Recession, the US unemployment rate peaked at around: (a) 12.1 percent (b) 25.8 percent (c) 9.5 percent (d) 6.7 percent (e) 10 percent 2 This study source was downloaded by 100000881534062 from CourseHero.com on 05-19-2024 19:11:29 GMT -05:00 https://www.coursehero.com/file/193350263/MT22017SketchSolutionspdf/

PART B: Written Questions QUESTION 1 - 23 marks The Romer model can be described by 4 equations: Y t = A t L y,t (1) Δ A t +1 = ¯ zA t L a,t (2) L y,t + L a,t = ¯ L (3) L a,t = ¯ l ¯ L (4) Y is final output, A is ideas/knowledge, L y is employment in the production of final output, L a is the number of researchers and ¯ L is the population. (a) What are the endogenous variables? What are the exogenous variables and the parameters? (5 marks) Answer : Endogenous: output Y , ideas A , final output labor L y , researchers L a . Exogenous variables and parameters: population ¯ L , ¯ z , the productivity of research (how e ↵ ectively researchers generate new ideas), ¯ l , the share of population engaged in research, A 0 , the initial stock of ideas. (b) Provide an economic explanation of each of the 4 equations. What is the driver of long-run growth in this model? (6 marks) Answer : The first equation is the production function for final output. It states that final goods are produced by combining ideas and labor. There are increasing returns to scale to objects and ideas. There are constant returns to scale to objects (labor) alone. The second equation says that ideas are accumulated based on the existing stock of ideas and the number of researchers. The third equation says that everyone employed in research, plus everyone employed in final production must equal the population. The final equation explains how labor is allocated across sectors. This says that there is a constant fraction ( ¯ l ) of the population employed in the research sector. Long-run growth in this model is generated by growth in ideas, A . (c) Show that the growth rate of output per person is equal to ¯ z ¯ l ¯ L . If ¯ l = 0 . 04, ¯ z = 1 / 2000 and ¯ L = 1000, what is the growth rate of output per person? (6 marks) Answer: This was covered on assignment 4. Substitute equations 3 and 4 into equation 1, then divide by ¯ L .This yields y t = Y t / ¯ L = A t (1 - ¯ l ). Using the growth rules from Chapter 3, the growth rate of output per person equals the growth rate of ideas: g y = g a because the term (1 - ¯ l ) is a constant. Next, divide equation 2 by A t and substitute equation 4. This yields g a = Δ A t +1 /A t = ¯ z ¯ l ¯ L , and we found that g y = g a , so the growth rate of output per person is ¯ z ¯ l ¯ L . Using the numbers: g y = 0 . 04 ⇥ (1 / 2000) ⇥ 1000 = 0 . 02 or 2%. (d) A government scheme successfully attracts more workers into the research sector. How would you study the e ↵ ect of this policy change using the Romer model above? Using a graph of output per person (on a ratio scale), what happens to the level and growth rate of GDP per person over time. Explain. (6 marks) Answer: Assuming the scheme does not bring in workers from abroad, the increased incentive to become a researcher raises the number of researchers and lowers the number of workers in fi- nal goods production. This could be modeled as a rise in ¯ l . This has two e ↵ ects. First, from 4 This study source was downloaded by 100000881534062 from CourseHero.com on 05-19-2024 19:11:29 GMT -05:00 https://www.coursehero.com/file/193350263/MT22017SketchSolutionspdf/

y t = Y t / ¯ L = A t (1 - ¯ l ), the level of output per worker initially falls as fewer people are producing final output. But, second, more researchers leads to a faster growth rate of ideas, and therefore of output per person. Although output per person drops initially (as shown by the level drop in the chart below), the growth rate is faster (as shown by the steeper slope, this is a ratio scale chart). Output per person (ratioscale) Time !"# %&ℎ"(" Old growth path New growth path 5 This study source was downloaded by 100000881534062 from CourseHero.com on 05-19-2024 19:11:29 GMT -05:00 https://www.coursehero.com/file/193350263/MT22017SketchSolutionspdf/

QUESTION 3 - 24 marks Consider the Phillips Curve from the simple short-run model we studied (in Chapter 9): Δ ⇡ t = ¯ v ˜ Y t , where ⇡ is inflation, ˜ Y is short-run output and ¯ v is the slope of the Phillips Curve (a parameter). Suppose the economy has been hit by a shock that has left inflation at 6%, (for example, reflecting recent oil price increases). Actual output is equal to potential. You are the head of a central bank and you are considering how to deal with this situation. (a) Using a graph of the Phillips Curve, explain how you could reduce inflation over time? (6 marks) Answer: The Phillips Curve tells us that we can only reduce inflation if short-run output is set below 0. This means the policymaker needs to induce a recession to bring down inflation. As Y t < ¯ Y t , Δ ⇡ t < 0. Once inflation is at the desired level, we can set Y t = ˜ Y t again. Change in inflation Short-run output 0 0 ! " # <0 ∆% < 0 (b) Briefly provide two reasons why higher levels of inflation might be costly for an economy. (6 marks) Answer: The answer should cover any two of the costs of inflation discussed in section 8.4. It may also discuss the inflation tax or the costs of hyperinflations (section 8.5). More detailed answers will gain more marks. (c) Suppose you want to reduce inflation to 3%, no later than 3 years from now. Your sta ↵ produce the following three policy plans for you to consider: Short run output Inflation Option Year 1 Year 2 Year 3 Year 1 Year 2 Year 3 1 -6% 0 0 3% 3% 3% 2 -4% -2% 0 4% 3% 3% 3 -2% -2% -2% 5% 4% 3% If you cared primarily about the e ↵ ect on inflation, which option would you recommend and why? If you cared primarily about the e ↵ ect on output, which option would you recommend and why? (6 marks) 7 This study source was downloaded by 100000881534062 from CourseHero.com on 05-19-2024 19:11:29 GMT -05:00 https://www.coursehero.com/file/193350263/MT22017SketchSolutionspdf/

Answer : If we care about low inflation, then we want option 1. That gets us to our goal quickly. If we only care about the cumulative lost output, then we can’t decide between the three options. In all three cases, all three years of lost output adds up to 6 percent. The real question is, Do we want a quick sharp recession, or a slow draining one? Option 1 is likely to cause the sharpest fall in unemployment (recall Okun’s law), and it may therefore be desirable to smooth the e ↵ ect over the three years. Option 3 provides the least volatility in output, although it will take longer to get inflation down to 3%. If we care most about minimizing the level of unemployment, option 3 might be the better option. There is a trade-o ↵ between protecting output and lowering inflation. This is because the only way to bring down inflation is to generate a recession. (d) According to the numbers in the table above, what is the slope of the Phillips Curve, ¯ v , in this economy? If ¯ v were lower, would it be more or less costly to reduce inflation? Explain. (6 marks) Answer : The slope is +1 / 2. Consider option 1, year 1: short-run output is - 6% and inflation falls from 6 to 3%. Since the Phillips Curve is Δ ⇡ t = ˜ v ˜ Y t , - 3 / - 6 = +1 / 2. In year 2 and year 3, short-run output and the change in inflation are both 0, so we can’t use years 2 and 3 to work out the slope. Using the other options (2 and 3), will also give you a slope of +(1 / 2). For example, in option 2 year 1, short-run output is -4% and inflation falls from 6 to 4%. - 2 / - 4 = +(1 / 2). In year 2, short-run output is -2% and the fall in inflation is 1%. In option 3 short run output is always -2% and inflation falls 1% in each year. If ˜ v were smaller, the same change in short-run output would lead to smaller changes in inflation. This means you would need to create a larger recession to bring down inflation at the same rate. If you care about output, reducing inflation will now be more painful. 8 This study source was downloaded by 100000881534062 from CourseHero.com on 05-19-2024 19:11:29 GMT -05:00 https://www.coursehero.com/file/193350263/MT22017SketchSolutionspdf/ Powered by TCPDF (www.tcpdf.org)