**INTERMEDIATE
MACROECONOMICS: PROBLEM SET #1 ANSWERS**

Jan 31 2003

*Chapter 2.*

__Q: 12__: Increased production by 500,000 will, by definition
increase national income by 500,000 also.
That is, we must account for the full increase in the output.

a) Income rises from 1,000,000 to Y = 1,500,000.

b) Since the question notes that only 450,000 will be
spent, we can assume that

consumption rises by 450,000 to 1,250,000.

c) Saving: Money not spent on
consumption is saved. Thus, saving increases by the 50,000 that is NOT
consumed. S = 250,000

d) Investment: must rise by
50,000 to match savings. It takes the form of inventory accumulation or
purchases of the goods produced but not purchased by consumers. I = 250,000

__Q. 13: __ How does the
relationship between S and I change before and after 1983? Use the leakage and injection relationship
to answer the question, and since we want to focus on S and I, set it up as
follows:

S – I =
(G-T) + NX

Then we can see easily that
prior to 1983 Govt budget deficits are positive and NX is positive (a trade or
current account surplus). Under these
conditions, we know that the (S – I) must be positive and equal to the trade
surplus plus the budget deficit. After
1983 when the trade balance became negative, (S – I) could be positive or
negative, but whatever the gap, it had to equal the difference between the twin
deficits.

**Problems, Chapter 2:**

1) a) GDP is most easily
found by noting that GDP = national income which equals

C + I + G + NX. C, G, and NX are easily found. I is a bit
trickier and is the sum of net fixed investment + depreciation (to get gross or
total investment) + inventory change. These sum to 668.6. The total GDP is:

== ** 3989.1**
{Note: You do not include the various tax categories.]

b) GNP: GDP modified by
receipts from and payments of factor income to rest of world.

GNP
= 3994.1

c) NDP = GDP - depreciation =
3550.6

d) Domestic Income = NDP -
indirect business tax = 3211.4

e) Personal Income = Dom
Income adjusted for transfers, SS taxes, undist. profits and including personal
int. payments = 3380.1

f) Disposable Pers. Income =
Personal Income - taxes = 2887.4

g) Personal Savings = Disp.
Income - Consumption = 305.3

3) On GDP deflators:

a) The table:

Nom GDP: $20
million cars + $30 million PC = $50 million in year 1

$22 million cars + $10.5 million PC
= $32.5 million in year 2

Const. $ ExP

Year 1 Prices $50
mill. year 1 $65 million year 2

Year 2 Prices $$29
mill year 1 $32.5 mill year 2

b) Chain weighted % change in
real GDP from year 1 to 2:

% Change in real GDP in year
1 prices = GDP in year 2 in year 1
price which is $65 divided by GDP in year 1 which is $50 = 1.3
or a 30% increase.

% Change in real GDP in Year
2 prices = 32.5/29 = 1.12 or an 12% increase.

Take square root of the
product of the two ratios to get the geometric average = 1.2066 for a

__chain weighted % change
of 20.7%.__

c) Chain weighted GDP
deflator: Deflator is the nominal divided by real GDP. The nominal GDP in year 2 = $32.5. The chain weighted REAL GDP in year 2 is $60
million.

[Note, this is the nominal GDP in year 1 of plus the 20% real
chain weighted rate of growth we calculated in part a. $50 million plus 20% of 50 = 60. Also note that we
are implicitly setting year 1 = 1 in this process by calculating the rate of
growth from year 1 to year 2 in part b – that is, the rate of growth of 20% is
measured from year 1 which becomes the starting point of the “1” from which the
1.2 arises.]

The chain weighted deflator
is therefore 32.5/60 = .54 indicating that prices in year two are only 54% of
what they were in year 1. That is,
there has been DEFLATION between year one and year two. This is obviously because of the dramatic
drop on computer prices.

You can also do this by
setting the price level = to 1 in each year and noting how the GDP changes as
you value the quantities as year 2 prices. For example, year 1 quantities X
year 1 prices = $50 million. Year 1 quantities at year 2 prices = $29 mill. The
ratio of the second to the first is .58 meaning that GDP in year one measured
in year 2 prices would only have been 58% as high as it was. Do the same for year 2 and you get .5 , then
take the geometric average of year of both deflators and you get the chain weighted
deflator of .54.

d) The implicit price deflator for year 2 is the ratio of the nominal to the real chain weighted real GDP in year 2. Nominal GDP in yr 2 is $32.5 mill and the real chain weighted GDP in year 2 is $60 million, as above (20% growth). The ratio of these two is: 5416 or very close to the deflator we just found.

5) Growth rates: Basically,
calculate the change from period to period, divided by the original magnitude
to get a % change. Then, since we want to project quarterly changes to an
annualized rate, multiply the change by 4 [4 quarters = a whole year...] You
can also use the formula on page 51 and you=ll
get the same answers.

8) Unemployment rate =
U/Un+employment [the labor force] == 6.7%

9) Okun’s law says that Unem.
.5% lower than it otherwise would be, for every % increase in Y/Y^{n}
(ie. for every % increase in Y). As
unemployment is .7% above its average (or “natural”) rate, Y/Y^{n}
should be below 100% by twice that, or 1.4

If
you solve the Okun equation, U = 6 -
.5[100(Y/Y^{n}) – 100] when U = 6.7, you will see that Y/Y^{n}
is .986 which means that actual output is only 98.6% of potential or that it is
1.4% below potential, as we exptected.

When Y/Y^{n} = .986
we divide the actual GDP in 1991, $6079 billion by .986 to see that potential
GDP in 1991 was which leads to the conclusion that the nat. real GDP is 6165.3
bill. which tells us that there was a LOSS of about $86.3 billion in GDP due to the higher
unemployment rate.

**SUPPLEMENTARY QUESTIONS: **

** **

**A) **If Saving out of income increases where S + T = I + G + NX , while the budget
must be balanced, then:

S = (G – T) + I + NX
assuming G – T = 0.

Then: an increase in S must
increase I + NX which is the TOTAL investment (domestic plus foreign. So, the trade balance must increase (unless
offset by an even more rapidly rising I).

B)

a) NDP = GDP -
depreciation. Depreciation is the gap
between gross and net investment = 600. NDP = 6000-600 = 5400.

b) Net Exports: GDP = C + I +
G + NX, or

NX = GDP - C – I - G = 6000 -
4000 – 800 - 1100 = **100**

c) Taxes minus transfers or
net taxes: budget surplus is T-G =
30. Since G = 1100, T = **1130**.

d) Disposable personal
income: Net Domestic Product (income)
minus total net taxes 5400 - 1130= 4270

e) Personal saving two ways
of looking at this: One is to deduce C from Personal Disposable income: 4270 – 4000 = 270.

The other is to plug numbers
into our equality:

I + G + NX == S + T ==
NX + (G-T) = S-I . Use results
from above.

100 - 30 = S - 800** S = 870 **[note: this includes gross
investment. If we used net investment of 200 instead, this would also be 270 as
above].

C) Points below the Okun’s
law trend line indicate that the level of unemployment is lower than Okun’s law
predicts for a given level of output.
Note, if the relationship between a change in GDP relative to potential,
Y/Y^{n}, and U had changed, we would expect to see a new SLOPE of the
line. This doesn’t appear to be the
case. Rather, a set of points lies
below the line, as if the line should SHIFT down [shifts vs. slopes rear once
again!]. The only way for the entire line to shift, is if the average (or long
run or so-called “natural rate” of unemployment) is now lower than it used to
be. This appear to have happened in the 1990s. We will leave why this may have
happened unexplained for now.