Background
We can deflate "raw" (or nominal) economic data with the use of a price
index. The price index may measure consumer price changes (CPI),
overall price changes (GDP deflator index), or whatever. Any such
index would be constructed by taking information from two or more years
on what the prices actually were. Then wel compute the price index by valuing
a constant set of products (2 of this, 5 of that, etc.) by the price in
the early year and in the later year. The "basket of physical commodities"
can be one which corresponds to the early year or, alternatively, the later
year. For example, the CPI uses a early market basket which supposedly
is based on how much of each item families bought at that time. The
book discusses how inflation estimates can be biased up or down, depending
on whether the basket for the early or later year is used. The GDP
deflator index used the later year.
Once you have the overall price for the market basket in the two years, one is declared to be the base year and is assigned 100 as an index number. The other year will get the index number which represents the percent relationship to the base year. For example if the first year is chosen as base, and the overall basket price is 50 percent higher in the later year, the index number will be 150.
If there are more than two years, each other year is figured out the same way, by comparing to the base year..
The deflation process is easy once we have the index numbers. Divide the uncorrected figure, say GDP, by the decimal equivalent of the index number. The result is "real" GDP. It is the same, in principle, as if we went back to each year's GDP and repriced everything in terms of base year prices, then added up the GDP all over. Any year with an index number smaller than 100 will experience a real GDP larger than the raw GDP, for years with larger index numbers, the raw GDP will exceed real GDP. The important effect is that the real GDP for any year can be compared to each other year to see the physical difference in output -- the smokescreen of price changes has been removed.
This process is now done in a more sophisticated way by the US Commerce Department. A chain weighted approach is used so that a smaller bias results, with a geometric average being computed. It is very much more difficult to understand what is being accomplished.
The Problem
Here is a GDP/real GDP problem which is easier than the Case and Fair
material, and is based on the discussion above. Be sure to look at
the CPI material in the relevant chapter of the text, if you are uncertain.
The assumption below is that there are only two goods produced and consumed
in this economy. All price indeces are to be calculated
with '97 as the base year.
Try your best to get some answers before class
this week. Those who have answers to turn in will get credit for
it (if so, make a copy to turn in and one to keep).
BASIC DATA
GOOD 1
GOOD 2
Value of
QUANT. MARKET
| QUANT. MARKET
Tot. Output
YEAR PRODUCED PRICE PxQ |
PRODUCED PRICE PxQ
1997 80
2.00 160.00 | 40
2.00 80.00
240.00
1998 90
3.00 270.00 | 50
4.00 200.00 470.00
COMPUTATIONS
Tot. Output
97 QUANT @ '98 PRICE 240.00 | 97
QUANT @ '98 PRICE 160.00 400.00
98 QUANT @ '97 PRICE 180.00 | 98
QUANT @ '97 PRICE 100.00 280.00
Questions: using the two commodities, 1)compute the price index the
way the CPI is done; 2) then calc. nominal GDP for 97, and 98;
3) then calculate the GDP deflator index ; 4)then
compute real GDP for 98.
Also, given that the capital stock increases by 50 units in 98
and good 1 is "capital", what is real gross investment, real depreciation,
and
real net investment in 1998 (stated in 1997 prices).