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Spring 2014 Econ 2 From Sample Final Exam I

Spring 2014 Econ 2 From Sample Final Exam I. J. Bradford DeLong U.C. Berkeley. A. Identifications.

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Spring 2014 Econ 2 From Sample Final Exam I

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  1. Spring 2014Econ 2From Sample Final Exam I J. Bradford DeLong U.C. Berkeley

  2. A. Identifications • Identifications (20 minutes—if you are not through after 20 minutes, skip to the next question): Briefly, in one or two sentences, explain the terms set out and how they have been used in the course: • 1. Supply and Demand Curves • 2. Consumer and Producer Surplus • 3. Pigovian Taxes • 4. Price Ceilings and Price Floors • 5. Willingness-to-Pay • 6. Opportunity Cost • 7. Planned Expenditure • 8. Inflation

  3. B. Our Bread and Butter… • Introduction: In the central part of the state of Euphoria there is a small city, Avicenna, which is the home of Euphoric State University. [“Avicenna” is a corruption of the Arabic Ibn Sina, the byname of the great eleventh-century Iranian Abu Ali al-Husayn ibn Abd Allah ibn Sina: academic administrator, Quran reciter, astronomer, chemist, geologist, psychologist, theologian, mathematician, physicist, physician, poet, and paleontologist.] We will look at the daily market for espresso-based drinks in Avicenna.

  4. B. Our Bread and Butter II • Setup: Suppose that the quantity of espresso drinks demanded and the quantity of espresso drinks supplied daily are given by the equations: • Demand: Q = 20,000 - 2000P • Supply: Q = max(-16000 + 8000P, 0) • where P is the price of an espresso-based drink in dollars: • What is the market equilibrium price? What is the market equilibrium quantity? What is the producer surplus? What is the consumer surplus? Explain, intuitively, why the distribution of producer and consumer surplus is what it is. What would the distribution of consumer and producer surplus be if the supply equation were: P = 3.6?

  5. Transform the Equations • We need to get the equations into our standard form: • Demand: Q = 20,000 - 2000P • Q/2000 = 10 - P • P = 10 - Q/2000 • Supply: Q = max(-16000 + 8000P, 0) • Q/8000 = max(-2 + P, 0) • P = 2 + Q/8000

  6. B.1&2. What Is the Equilibrium Price and Quantity? • Demand: P = 10 - Q/2000 • Supply: P = 2 + Q/8000 • Set the demand and the supply prices equal to each other: • 10 - Q/2000 = 2 + Q/8000 • 80000 - 4Q = 16000 + Q • 64000 = 5Q • Q = 12800 • Plug back into the demand and supply curves: • Demand: P = 10 - Q/2000 = 10 - 12800/2000 = 10 - 6.4 = 3.6 • Supply: P = 2 + Q/8000 = 2 + 12800/8000 = 2 + 1.6 = 3.6

  7. B.3. What Is the Consumer Surplus? • Demand: P = 10 - Q/2000 • Supply: P = 2 + Q/8000 • Q = 12800; P = 3.6 • Average willingness to pay: AWtP = avg(10,3.6) = 6.8 • CS = (AWtP - P) x Q = (6.8 - 3.6) x 12800 = 40960

  8. B.4. What Is the Producer Surplus? • Demand: P = 10 - Q/2000 • Supply: P = 2 + Q/8000 • Q = 12800; P = 3.6 • Average opportunity cost: AOC = avg(2,3.6) = 2.8 • PS = (P - AOC) x Q = (3.6 - 2.8) x 12800 = 10240

  9. B.5. Explain, Intuitively, Why the Distribution of Producer and Surplus Is What It Is • Demand: P = 10 - Q/2000 • Supply: P = 2 + Q/8000 • Q = 12800; P = 3.6 • PS = 10240; CS = 40960 • Why? Supply is elastic. • That means that there are always a lot of potential suppliers out there with opportunity costs only a little bit more than the current price • That means that market competition among suppliers thinking of entering and entering is very strong, leaving little opportunity for an average supplier to get much of a wedge between her opportunity cost and the price she can charge

  10. B.6. What Would the Distribution of Consumer and Producer Surplus Be if the Supply Equation Were: P = 3.6? • Same equilibrium market price, same demand curve, so CS is the same: CS = 40960 • AOC is always 3.6. That’s the price. There is no wedge between price and opportunity cost anywhere—so there is no producer surplus

  11. C. Elasticity • Setup: Still in Avicenna, but different supply and demand curves • Demand: P = 148.413 x Q(-0.5) • Supply: P = 1/54.598 x Q • What is the elasticity of demand at Q = 1? What is the elasticity of supply at Q = 1? What are the market equilibrium price and quantity? What are the producer and consumer surplus? At what quantity is total revenue maximized?

  12. C.1. What Is the Elasticity of Demand at Q=1? • Demand: P = 148.413 x Q(-0.5) • dP/dQ = -74.2065 x Q(-1.5) • dP/dQ(Q=1) = -74.2065; dQ/dP = -1/74.2065 • P/Q(Q=1) = 148.413 • (P/Q)(dQ/dP) = 148.413 x (-1/74.2065) = -2 • Or you could have simply looked at the exponent on Q, and inverted it…

  13. C.2. What Is the Elasticity of Supply at Q=1? • P = 1/54.598 x Q • dP/dQ = 1/54.598 • dP/dQ(Q=1) = 1/54.598; dQ/dP = 54.598 • P/Q(Q=1) = 1/54.598 • (P/Q)(dQ/dP) = 1 • Or you could have simply looked at the exponent on Q, and inverted it…

  14. C.3&4. Equilibrium Price and Quantity • Demand: 148.413 x Q(-0.5) • Supply: P = 1/54.598 x Q • Easiest to take logs: • ln(P) = 5 - 0.5ln(Q) • ln(P) = -4 + ln(Q) • ln(Q) = 9/1.5 = 6; Q = 403.4 • ln(P) = 2; P = 7.389

  15. C.5. Producer Surplus • Supply: P = 1/54.598 x Q • ln(Q) = 9/1.5 = 6; Q = 403.4 • ln(P) = 2; P = 7.389 • What is the average opportunity cost? • Linear supply curve: so AOC = 3.6945 • PS = (P - AOC) x Q = (7.389 - 3.6945) x 403.4 = 1490.4

  16. C.6. Consumer Surplus • Demand: 148.413 x Q(-0.5) • ln(Q) = 9/1.5 = 6; Q = 403.4 • ln(P) = 2; P = 7.389 • What is the average willingness to pay? • At Q = 0, WTP = ∞ • Even worse, WTP is not a linear function of quantity: even if you had a maximum WTP, you could not simply average it with the price • What to do?

  17. C.6. Consumer Surplus II • Demand: 148.413 x Q(-0.5) • ln(Q) = 9/1.5 = 6; Q = 403.4 • ln(P) = 2; P = 7.389 • This is why we want you to have calculus… • CS =TWtP - P x Q

  18. C.6. Consumer Surplus III

  19. C.7. At What Quantity Is Total Revenue Maximized? • Demand: P = 148.413 x Q(-0.5) • Elasticity of -2 everywhere • That means that every time you reduce the price by 1%, you increase the quantity by 2% • So you increase the revenue by 2% - 1% = +1% • The more is sold, the more the revenue: this is a consequence of an elasticity larger in absolute value than -1, and this demand curve has an elasticity of -2 everywhere

  20. D. Externalities • Externalities can be subtle… • Let us move across the bay and 60 miles south from Avicenna to the town of Tall Stick, home of Crony Capitalism University… • The 10,000 students at CCU do two things with their disposable incomes of $5,000/year each: • Buy gourmet pizzas at $20/pizza • Rent BMWs at $5000/year • Utility of each student: • U = (number of pizzas) + 500(if renting BMW) - (1/20)(number of other students renting BMWs) • This utility function thus has both envy and spite…

  21. D.1. If Nobody Rents a BMW… • What is the utility of a typical student? • MEMO: Utility of each student: U = (number of pizzas) + 500(if renting BMW) - (1/20)(number of other students renting BMWs) • A student who buys 250 pizzas has a utility = + 250. • Since nobody rents a BMW, the “envy” term is 0 • So 250

  22. D.2. If Nobody Else Is Renting a BMW… • How does a typical student spend his or her money? • What is his or her utility (measured in pizzas)? • MEMO: Utility of each student: U = (number of pizzas) + 500(if renting BMW) - (1/20)(number of other students renting BMWs) • If the student rents a BMW instead of buying pizzas, his or her utility goes up by 500 - 250 = + 250 pizzas. The opportunity cost of renting a BMW is 250 pizzas—and the utility derived is considerably more than that, as his or her WtP is 500 pizzas • U = 500

  23. D.3&4. If Everybody Else Is Renting a BMW… • How does a typical student spend his or her money? • What is his or her utility (measured in pizzas)? • MEMO: Utility of each student: U = (number of pizzas) + 500(if renting BMW) - (1/20)(number of other students renting BMWs) • If the student rents a BMW instead of buying pizzas, his or her utility goes up by 500 - 250 = + 250 pizzas. The opportunity cost of renting a BMW is 250 pizzas—and the utility derived is considerably more than that, as his or her WtP is 500 pizzas • U = 500 (from own consumption) - 1/20 x 9999 = + 1/20

  24. D.5. Since It Made Sense for Each Student to Rent a BMW… • How come everybody renting BMWs reduced average utility from 250 to 1/20 (if, that is, you got D.1. and D.4. correct)? • MEMO: Utility of each student: U = (number of pizzas) + 500(if renting BMW) - (1/20)(number of other students renting BMWs) • 499 99/20 of the utility from renting a BMW comes from spite and envy: the transfer of utility to those who have and know that others have not (the spiteful) from those who have not and know that others have (the envious). • Only 1/20 of a utility unit is created for society as a whole by renting a BMW. • This psychological externality means that the market gets it wrong: private incentives to rent BMWs are radically divergent from societal incentives

  25. D.6. What Is the Optimal Externality-Compensating Pigovian Tax on BMW Rentals at Crony Capitalism University? • Since 499 19/20 pizzas’ worth of the utility from BMW rental is an externality, and since pizzas cost $20 each, the appropriate tax on BMW rentals is $9,999

  26. E. “Envy” • Back in January 2012 Republican presidential candidate Mitt Romney said: • You know, I think it's about envy. I think it's about class warfare. When you have a President encouraging the idea of dividing America based on the 99 per cent versus one percent—and those people who have been most successful will be in the one per cent—you have opened up a whole new wave of approach in this country which is entirely inconsistent with the concept of one nation under God. The American people, I believe in the final analysis, will reject it… • This is an argument that when we do benefit-cost calculations with a utility function like: • U = (number of pizzas) + 500(if renting BMW) - (1/20)(number of other students renting BMWs) • We should count the first two terms and add them up as parts of our social welfare function and throw away the third term. • Write a short essay of three paragraphs: the first paragraph should set out what are, in your estimation, the strongest reasons for rejecting Mitt Romney’s argument; the second paragraph should set out what are, in your estimation, the strongest reasons for Mitt Romney’s argument; and the third paragraph should choose a side and explain why you chose the side you did.Utility of each student: U = (number of pizzas) + 500(if renting BMW) - (1/20)(number of other students renting BMWs)

  27. E. “Envy” II • So what is our answer going to be? Strongest arguments for Romney…

  28. E. “Envy” III • So what is our answer going to be? Strongest arguments against Romney…

  29. E. “Envy” IV • So what is our answer going to be? Where we come down, and why…

  30. F. Macroeconomic Policy • Suppose that it is December 2016 and you are called to Washington to audition for a cabinet-level post in the next administration and to advise him on the proper size of the economic stimulus program. • Your forecast is that, were 2018 to be a normal business-cycle time, that the level of real GDP in 2018 would be $17.0 trillion/year. You are conducting your analysis in the income-expenditure framework where: Y = C + I + G + X , C = co + cy(Y - T). You believe that cy = 0.5. • You project that there will be little change from trend in consumer confidence co, which you project at $2 trillion/year in 2018. you project that business demand for investment spending will be $3 trillion/year in 2018. You project that exports will be $2 trillion/year in 2018. And you project that the Federal Reserve will not take additional steps to stimulate the economy.

  31. F.1. What Level of Government Purchases G Do You Recommend for 2018? Why? • With a multiplier of 2, you project that if nothing is done GDP will be $16 trillion/year in 2018, $1 trillion/year beneath potential • So you recommend a $500 billion/year stimulus program for 2018 to close the output gap

  32. F.2. Suppose That the President-Elect’s Political Advisors Say That It Is Very Important, Politically, to Cut Government Spending. What Do You Say in Response? • You then call for a $1 trillion/year temporary tax cut for 2018 • You point out that this program raises the national debt by more than a government purchases increase

  33. F.3. Collapse of Euro: Forecast of I Down from $3.5 to $2.5T/Year • What do you say? • You raise your recommended stimulus program to $750B/year

  34. G. Economic Growth • In 8300 BC there were roughly 5 million people in the world—with an average standard of living of about $500/year. In 1700 there were roughly 640 million people in the world—with an average standard of living of about $500/year. In 1900 there were roughly 1.6 billion people—with an average standard of living of about $1000/year. Today there are roughy 7.4 billion people— with an average material standard of living of $8000 dollars per year.

  35. G.1. Rule of 72: Pop and RGDP growth rates, 8300 BC-1700 • In 8300 BC there were roughly 5 million people in the world—with an average standard of living of about $500/year. In 1700 there were roughly 640 million people in the world—with an average standard of living of about $500/year. • 10000 years • 7 doublings of population, 7 doublings of real GDP growth • To get 7 doublings in 10000 years you need one doubling every 1428 years • 72%/1428 is roughly 0.05%/year

  36. G.2. Rule of 72: Pop and RGDP growth rates, 1700-1900 • In 1700 there were roughly 640 million people in the world—with an average standard of living of about $500/year. In 1900 there were roughly 1.6 billion people—with an average standard of living of about $1000/year. 200 years • A doubling of population, and then 25% growth—call it 1.2 doublings • To get 1.2 doublings in 200 years you need one doubling every 170 years • 72%/170 is roughly 0.4%/year • Call it 2.5 doublings of real GDP… • To get 2.5 doublings in 200 years you need one doubling every 80 years • 72%/80 = 0.9%/year

  37. G.3. Rule of 72: Pop and RGDP growth rates, 1900-2014 • In 1900 there were roughly 1.6 billion people—with an average standard of living of about $1000/year. Today there are roughy 7.4 billion people— with an average material standard of living of $8000 dollars per year. • 114 years • 2 doublings of population, and then 15% growth—call it 2.15 doublings • To get 2.15 doublings in 114 years you need one doubling every 53 years • 72%/53 is roughly 1.35%/year • Call it 5.15 doublings of real GDP… • To get 5.15 doublings in 114 years you need one doubling every 22 years • 72%/22 = 3.3%/year

  38. G.4. Comparing 1900-2014 to 8300 BC-1700 • 8300 BC-1700: Pop: 0.05%/year; RGDP: 0.05%/year • 1700-1900: Pop: 0.4%/year; RGDP: 0.9%/year • 1900-2014: Pop: 1.35%.year; RGDP: 3.3%/year • Population growth 27 times faster • RGDP growth 66 times faster

  39. G.5. Comparing 1700-1900 to 1900-2014 • 8300 BC-1700: Pop: 0.05%/year; RGDP: 0.05%/year • 1700-1900: Pop: 0.4%/year; RGDP: 0.9%/year • 1900-2014: Pop: 1.35%.year; RGDP: 3.3%/year • Population growth 3.4 times faster • RGDP growth 3.7 times faster

  40. G.6. Projecting Growth, 2014-2100 • 8300 BC-1700: Pop: 0.05%/year; RGDP: 0.05%/year • 1700-1900: Pop: 0.4%/year; RGDP: 0.9%/year • 1900-2014: Pop: 1.35%.year; RGDP: 3.3%/year • To 2100: at 3.3%/year, doubles every 22 years. 86 years until 2100—that is 4 doublings • Current RGDP = $8000/yr x 7.4B = $59.2T/year • Times 16 = $947.2T/year as total world real GDP in 2100

  41. G.7. Projecting Living Standards in 2100 • 8300 BC-1700: Pop: 0.05%/year; RGDP: 0.05%/year • 1700-1900: Pop: 0.4%/year; RGDP: 0.9%/year • 1900-2014: Pop: 1.35%.year; RGDP: 3.3%/year • From (F6), $947.2T/year as total world real GDP in 2100 • 10B people: $94,720/year as average real income per capita in 2100

  42. H. Next Time • This is the first time we have taught Econ 2 since 2007, so we are especially anxious for feedback. • Write a four-paragraph essay: • Pick one element of the course that you thought worked best, and explain why you thought it worked best. • Pick one element of the course that you thought worked badly but needs to be improved, and explain how you think it could be improved. • Pick one element of the course that you thought worked badly and should be dropped. and explain why it should be dropped. • And pick one topic not covered in the course that you think should be added, and explain why it should be added.

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