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/Yn (ie. for every % increase in Y).  As unemployment is .7% above its average (or “natural”) rate, Y/Yn should be below 100% by twice that, or 1.4

 

If you solve the Okun equation,  U = 6 - .5[100(Y/Yn) – 100] when U = 6.7, you will see that Y/Yn 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/Yn = .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/Yn, 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.