Answer Outline for Econ 302 Exercise Set 1

Course Instructor: Professor Leigh Tesfatsion
Date: 31 January 1996

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FIRST TAKE-HOME EXERCISE SET [9 Points Total]      L. Tesfatsion
DUE DATE:  Tuesday, Jan 30, 9:30 A.M.        Econ 302/Spring 96

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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?

NOTE:  See the copy of this answer outline on closed reserve
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.

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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.]

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.

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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.

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
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