Economics 302 001 Fall 2010 University of Wisconsin Madison Menzie D Chinn Social Sciences 7418 Problem Set 1 Due in lecture on Monday September 27th Be sure to put your name on your problem set Put boxes around your answers to the algebraic questions 1 Chain Weighting Suppose that the agrarian economy of Simpsonia consists only of two sectors private consumption and private investment The following figures give total production and prices for both sectors in 2050 and 2051 The base year is 2050 CONSUMPTION 2050 2051 POTATOES Quantity 100 100 RICE Quantity 150 400 Price 3 4 Price 5 1 INVESTMENT 2050 2051 TRACTORS Quantity 4 5 SHOVELS Quantity 13 15 Price 100 130 Price 25 30 1 1 Calculate nominal consumption investment and GDP for 2050 and 2051 1 2 Using the traditional method calculate real consumption for 2051 1 3 Using the traditional method calculate real investment for 2051 1 4 Using the traditional method calculate real GDP for 2051 1 5 Does 2051 real GDP equal the sum of real consumption and real investment in 2051 when calculated using the traditional method 1 6 Using the chain weighted method calculate real consumption in 2051 1 7 Using the chain weighted method calculate real investment in 2051 1 8 Using the chain weighted method calculate real GDP in 2051 note develop weights for all four goods and take a weighted average of the growth rates 1 9 Does 2051 real GDP equal the sum of real consumption and real investment in 2051 when using the chain weighted method Explain why or why not 2 This problem requires obtaining data from various sources You can access the latest GDP data from the BEA at http www bea gov newsreleases national gdp 2010 pdf gdp2q10 2nd pdf August 2010 release The Consumer Price Index figures can be obtained from the St Louis Fed website at 1 http research stlouisfed org fred2 series CPIAUCSL cid 9 and http research stlouisfed org fred2 series CPILFESL cid 9 2 1 Calculate the annualized quarterly growth rate of real GDP in each of the last four quarters Is the economy expanding or contracting Show your work 2 2 Calculate the annual rate of change of the GDP deflator and the Personal Consumption Expenditure deflator from the second quarter of 2010 to the second quarter of 2010 Show your work Are they the same value 2 3 Calculate the annual rate of change in the Consumer Price Index All and the Consumer Price Index excluding food and energy from July 2009 to July 2010 using seasonally adjusted data Show your work Are the rates identical 3 Consider the following economy Eq No Equation 1 2 3 4 5 6 7 8 Y AD AD C I G X C a o bYd Yd Y T T TA0 tY I IN 0 G GO0 X g0 Description Output equals aggregate demand an equilibrium condition Definition of aggregate demand Consumption function a0 1200 b 0 8 Definition of disposable income Tax function TA0 800 t 0 15 Investment function IN0 1000 Government spending GO0 1000 Net Exports g0 200 3 1 Express in algebraic symbols the equilibrium level of income Y0 in this economy Show your work 3 2 Substituting in the numerical values given above indicate the numerical value of equilibrium income in this and future subsequent numerical answers round off your answer at two decimal places 3 3 Using the Keynesian Cross diagram illustrate your answer in part 3 1 with all relevant curves intercepts and slopes indicated clearly 3 4 Once again using algebraic symbols calculate the government spending multiplier in this economy What is the government transfers multiplier recall that a government transfer is the opposite of taxes Why are they different 3 5 Using the answer to part 3 2 what is the level of consumption spending in this economy 3 6 If the level of investment spending were to fall to 800 what would be the equilibrium level of income 4 Using the same economy as described in question 3 answer the following given that the budget surplus is BuS T G TA0 tY GO0 2 Assuming there is no government debt 4 1 What is the value of the budget surplus when investment spending is 1000 4 2 What is the budget surplus when I falls to IN1 800 4 3 What accounts for the change in the budget surplus from part 4 1 to 4 2 4 4 Suppose potential GDP or full employment GDP Y is 13000 What is the fullemployment or structural budget surplus BuS when I 1000 800 4 5 Can you write out what the BuS depends upon algebraically i e using the symbols rather than the numbers What variables affect BuS What variables affect the full employment budget surplus Bus 5 Suppose the government spending function is different G GO 0 Y where is a parameter This means that as the economy grows government spending on goods and services such building roads and buying tanks decline For purposes of answering the below questions assume the rest of the economy is the same as in question 4 5 1 Solve out for equilibrium income using algebraic symbols 5 2 What is the new government spending multiplier Y GO algebraically 5 3 Why is the new multiplier less than the standard one intuitively 5 4 Substituting in the parameter values what is the numerical value of the multiplier for 0 10 5 5 In this new economy what are i the parameters ii the exogenous variables iii the endogenous variables 6 National savings identity and the Keynesian Model Suppose equation 8 in the model in problem 3 looks like 8 X g 0 mY Net Exports 6 1 Solve for the impact of a lump sum tax increase on the trade balance or net exports algebraically 6 2 Using the definition of the budget surplus in problem 4 solve for the impact of a tax increase on the budget balance algebraically 6 3 Will the budget and trade balances move in the same direction in response to a tax increase e302ps1 f10 doc 13 9 2010 3