ANSWER OUTLINE FIRST TAKE-HOME EXERCISE SET [9 Points Total] L. Tesfatsion DUE DATE: Tuesday, Jan 30, 9:30 A.M. Econ 302/Spring 96 --------------------------------- --------------------------------- EXERCISE 1 [3 Points]: Hall and Taylor, Chapter 1, MACROSOLVE Exercise Number 1, page 30. (Experience using the PLOT option.) Plot and tabulate the annual GNP gap using the PLOT routine for MACROSOLVE. Identify the years when troughs and peaks occur. Based on this data, answer the following questions: (a) On average, how frequent are recessions (periods of time when the GDP gap is negative)? Has this frequency increased or decreased since the Second World War? Why might this frequency have changed? (b) Are business fluctuations symmetric? In other words, is the period of decline between peaks and troughs longer or shorter than the upswing from troughs to peaks? Can you think of a reason for this? ANSWER OUTLINE FOR EXERCISE 1: NOTE: See the copy of this answer outline on closed reserve (Reading Room, Heady 368) for the tabulated and plotted information upon which this answer outline is based. From the PLOT tabulated data for the U.S. real GDP gap for 1930-1993, "significant" peaks and troughs occurred as follows. (When more than one year is mentioned, it means that these years do not appear to be "significantly different" in terms of their measured real GDP gaps): PEAKS TROUGHS YEARS BETWEEN RECESSIONS (TROUGHS) 1930 1933 1937 1938 5 1944 1949 11 1951-3 1958-61 10 1968 1970-1 9 1973 1975 4 1978 1982 7 1986 1991 9 PART (a): Based on this data, the average frequency of recessions over 1930-1991 is approximately once every 8 years. Moreover, although pre-WWII (pre-1940) data are minimal here, the time between recessionary episodes appears to be longer after WWII. Economists (particularly of the Keynesian persuasion) have argued that this improved economic performance is due to the U.S. Federal government taking a more active role in maintaining high employment and low inflation in the years following WWII. PART (b): Based on this data, the average peak-to-trough (recessionary) period is approximately 3.5 years whereas the average trough-to-peak (expansionary) period is 4.7 years. Thus, upswings (expansionary periods) appear to be somewhat longer than downswings (recessionary periods). This may be a consequence of the underlying growth in the U.S. economy stemming from increases in capital and labor (both quantity and quality) and to general technological improvements. ------------------------------------------------------------------ BASIC REFS FOR NEXT 2 EXERCISES: HT Chapt 2, Lecture Notes HT2 EXERCISE 2 [3 Points]: Suppose you are given the following data on an economy for year T, all in nominal (current dollar) values: Gross domestic product = $1000 Government purchases of final goods and services = $200 Government saving = - $50 Private saving = $250 Gross investment = $150 Net factor payments and transfers from ROW = $0 Calculate the nominal values for (a) consumption; (b) disposable income; and (c) net exports. Show your work. [Hint: Use the national income accounting identity and the definitions for the terms listed on the left, plus a bit of algebra.] ANSWER OUTLINE FOR EXERCISE 2: The answer is: C = $600; Disposable income = $850; and NE = $50. These answers are obtained as follows. Consider the following accounting identities and definitions: (1) GDP = C + I + G + NE $1000 ? $150 $200 ? (2) I = S`p + S`g + S`r $150 $250 -$50 ? (3) S`p = [Y+V+F+N-T] - C $250 ? ? (4) S`r = -NE - V ? ? $0 From (2), it follows that S`r must equal - $50, hence it follows from (4) that NE = $50. Substituting NE = $50 into (1) gives C=$600. Finally, substituting C=$600 into (3) gives disposable income [Y+V+F+N-T] = $850. ----------------------------------------------------- EXERCISE 3 [3 Points]: Consider a closed economy E consisting of a fisherman named George (who fishes within the boundaries of E), a fishing boat-owner Fred who rents his boat to George, a group of laborers (George's boat crew members), and a government. Thus, George is the only producer of a final good or service. Suppose that George has the following expenses during year T: Boat rental: $15,000; and crew wages: $20,000. With his boat and crew, George catches 25,000 fish during year T. He sells all of the fish at the price of $2.00 each, so that his total receipts are $50,000. Receipts of $50,000 and expenses of $35,000 leave George with $15,000 profit. He then pays $5,000 to the government in taxes, leaving an after-tax profit of $10,000. Your goal is to find the GDP, measured in dollars, for this economy for year T. Show, numerically, how the spending approach, the product (value added) approach, and the total earned income approach provide three equivalent ways of calculating this GDP. Start by providing a verbal definition of each approach, and justify your calculations. ANSWER OUTLINE FOR EXERCISE 3: In accounting terms, George's situation for year T is as follows: Receipts $50,000 Less: Expenses 35,000 Equals: Before-tax profit 15,000 Less: Taxes 5,000 Equals: After-tax profit $10,000 By definition, the "spending approach" to measuring GDP in year T for the economy at hand, economy E, requires that one add up the amount spent by all purchasers of final goods and services produced during year T within the boundaries of E. George's customers spent $50,000 to buy his production of the final good fish---the only final good or service produced in E during year T. Consequently: GDP (spending approach) = 25,000 FISH x $2/PER FISH = $50,000 By definition, the "product (value added) approach" to measuring GDP in year T for economy E requires that one calculate the current market value of #all# goods and services produced by firms in E during year T, and then subtract from this value the current market value of any production by firms of goods or services used up in intermediate stages of production. Thus: GDP (value added = FIRM REVENUES FROM THE - FIRM PAYMENTS TO OTHER approach) SALE OF ALL PRODUCED FIRMS FOR GOODS AND GOODS AND SERVICES SERVICES USED UP IN DURING T INTERMEDIATE STAGES OF PRODUCTION DURING T = $50,000 + $15,000 - $15,000 fish boat rental George's payment to the (good) (service) boat rental company for boat rental services used up in his production of fish = $50,000 By definition, the "total earned income approach" to measuring GDP in year T for a HC requires that one add up all of the pre-tax income (wages, rent, interest, and profits) generated directly or indirectly by the production of final goods and services for year T that occurs within the boundaries of the HC (or equivalently, all of the after-tax income plus all tax revenues collected from this income). For economy E, the only final good or service produced within the boundaries of E is fish. Consequently, one needs to add up all of the pre-tax income generated directly or indirectly by the production of fish during year T, or equivalently, all after-tax income plus all tax revenues collected from the pre-tax income. Thus, GDP (earned income approach) = PRE-TAX WAGES + PRE-TAX RENT + PRE-TAX INTEREST + PRE-TAX PROFIT = AFTER-TAX WAGES, RENT, INTEREST, AND PROFIT + GOVERNMENT INCOME TAX REVENUES = $20,000 (crew wages) + $15,000 (boat rental fees) + $0.0 (interest) + $10,000 (George's after-tax profits) + $5,000 (gov't tax revenues) = $50,000 . NOTE: An alternative approach would be to interpret Fred's rental of his boat as a firm (owned by Fred) that sells a product called "boat services." In this case, George's payment of $15,000 to Fred would be considered the payment for a product produced by another firm rather than rental income. However, one would then have to interpret Fred's firm as producing profits of $15,000 which Fred receives as income. Consequently, adding up all after-tax wages, after-tax interest payments, after-tax rents, after-tax profits, and tax revenues generated directly or indirectly by the production of fish within the borders of E in year T, one would get GDP (earned income approach) = $20,000 (after-tax wages) + $0 (after-tax rents) + $0 (after-tax interest) +$25,000 (after-tax profits) + $5,000 (gov't tax revenues) = $50,000. The logic of the three approaches---spending, product (value-added), and earned income---is such that they must, by accounting definition, always give the same measure of total economic activity. Spending Approach = Product (Value Added) Approach By convention, unsold goods (inventories) are treated as if they were purchased by the firm which produced them. Consequently, given this convention, everything produced is sold, and the market value of all goods and services produced in a given period is by definition equal to what buyers must spend to purchase those goods and services. The spending measure of GNP measures spending on #final# goods and services, and so excludes spending on intermediate goods and services---i.e., goods and services used up in the production of other goods of services during the given period. But this is precisely what total value added measures, because: (a) it considers total revenues from the sale of all goods and services #produced by firms#, not households, implying that payments for labor services are not separately added in as "revenues" from the sale of labor services by households; and (b) it subtracts from this amount the market value (spending) on intermediate goods and services #purchased from other firms#, implying that payments for labor services are not subtracted. Thus, total value added indeed measures the total market value of #final# goods and services, and only these goods and services, without double counting. Product (Value Added) Approach = Earned Income Approach By accounting definition, firm revenues can be broken down into various uses of these revenues to cover costs of production and to provide profits to firm owners. Thus, Firm revenues = payments to other firms for intermediate goods and services (i.e., goods and services used up in the production of other goods and services) + Wage payments [payments for the labor services of employees] + Rental payments [payments for the services of real assets rented from other firms (e.g., real estate firms)] + Interest payments [payments for the services of money borrowed from other firms (e.g., banks)] + (Economic) profit [anticipated firm tax payments, anticipated firm dividend payments, anticipated firm depreciation expenditures, anticipated firm transfers (e.g., corporate gifts), plus residual "retained earnings"] . To measure economic activity via the production (total value added) approach, one adds together the revenues from the sale of goods and services of all firms (including real estate firms and banks), and then subtracts the payments of firms to other firms for goods and services used up in production. But, from above, this subtraction simply eliminates all #double-counting# of goods and services produced by firms, leaving (*) TOTAL VALUE = WAGES + RENT + INTEREST + (ECONOMIC) PROFIT ADDED = TOTAL EARNED INCOME .