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MIT 14 02 - Problem Set #1

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Problem Set 114.02: Introductory MacroeconomicsFebruary 15, 20041 Answer each as True, False, or Uncertain. Give a one or tw osen tence explanation for your answer.A) In the 1990s, the GDP of the United States grew more quickly than the GDP of Japan. A primaryreason for this was the lower unemploy ment rate in the United States during this period.B) Consider t wo countries, country A and country B. The en tire output of country A comes fromproducing widgets, a final good. The entire output of country B comes fr om selling gidgets, an interm ediategood in the production of widgets, to country A. If the value of country A’s widgets is $100 and country A’sGDP is $60, then country B’s GDP must be $40.C) The unemplo yment rate in Macronesia (a country) drops in one year from 8% to 7%, and thepopulation of people of working age remains the same. Therefore, there has been an increase in the numbe rof work ers who are employ ed in Macronesia.D) Macronesia enters an economic slump. There are t wo types of people in Macronesia, type 1 and type2. T ype 1 individuals save a greater share of an y income increases than do type 2 individuals. To have thebiggest effect on output, it would be best to target any tax cuts to the type 2 individuals.E) Corporate profits represent a larger share of US GDP than does wages paid to workers.F) Wanting to mak e its economy grow faster, the government of Mac ronesia decides to increase gov ern-men t spending. Macronesia also has a high inflation ra te. This expansionary fiscal policy will also have thebenefit of lowering Macronesia’s high inflation rate.(G) Suppose that Macronesia is in a rece ssion. To get out of the recession, it decides to decrease taxesthis y ear and then increase them by the same amount next year (the government is very concerned aboutdeficits). This policy (which is announced to the public) is gua ra nteed to help the recession by getting peopleto spend more today.2 Macroeconomic statisticsA) Consider Macronesia, a countrywiththreecompanies: Macrosoft,CompanyA,andCompanyB.Macrosoft makes Monopoly board games using boards and cards as its intermediate goods. Company Amakes cardboard. Compan y B makes boards and cards using cardboard. Their respectiv e balance sheetsare below.Compan y ARevenues $10Expenses: Wages $5Profit$5Compan y BRevenues $30Expenses: Wages $12Cardboard $10Profit$8MacrosoftRevenues $60Expenses: Wages $20Boards and cards $30Profit$101Show three different ways to compute the GDP of Macronesia.B) Consider the basic macroeconomic aggregate statistics for Macronesia, where the base year is 1999(GDP deflator=1).1999 2000 2001 2002 2003GDP $35 $40 $50 $55 $60GDP deflator 1 1.10 1.30 1.45 1.45U 5%4%5%6%4%Real GDP1) Fill in the line for real GDP in the table.2) When did the economy of Macronesia gro w the fastest in real terms?3) Does the data follow Okun’s la w ? Does it follow the Phillips curve?C) Suppose that Macronesia’s GDP can be decomposed as follows.GDP $100Personal consumption $40Private investment $40Go v ernmen t purc hases $20Net exports $0Describe how this table would change if Social Security payments to senior citizens increased by $5 andprivate in vestment decreased by $5 with no other ch anges. Would GDP increase, decrease, or stay the same?Assume that an y increase in Social Security pa ymen ts goes to personal consumption and that an y increasein transfers comes at the expense of other government purchases.3 Solving a Model of Consump tionThe economy of Macronesia is in equilibrium. Two conditions determine equilibrium in the Macronesiangoods market:1) Z = c0+ c1(Y − T )+I + G ,and2) Y = Z ,where: Z = total demand for goods, T = taxes,I = investment, G = government spending, and a, c0and c1are constants with 0 <c1<a<1.A) Assume that the go vernment runs a balanced budget (G = T ). Solve for the equilibrium level ofoutput. What effect does an increase in government spending hav e on equilibrium output (given that taxesincrease by the same amount)?B) Now assume that taxes are a constant fraction of income. What is the equilibrium output level?Again assume budget balance is maintained. What happens as the tax rate approaches one? Does thisseem realistic?C) Now consider the following modification to the basic model in A). As taxes increase, more of eachadditional dollar is lost to government waste. So the demand equation becomes: Z = c0+ c1(Y − T )+I +G −12T2,where12T2describes the amount of waste in Macronesia. What tax ra t e maximizes equilibriumoutput, given that G = T ?D) Depict equilibrium in the goods market for the economies described in A) and C), given equal, no nzerotax rates in


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MIT 14 02 - Problem Set #1

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