Crazy Mathematician is a street person who throughout recorded history has consumed only two goods, on which he spends all his income. The two goods are Macdonald's Big Macs and calculators. Weird graduate student Joe has been given data on Crazy Mathematician's average weekly consumption, and market prices, for the two goods for two years that Professor Idiot Psychologist followed Crazy Mathematician. The data are as follows:
1973 1993
Price Quantity
Price Quantity
#/week
#/week
Big Macs $0.50 30 $2.00 27
Calculators $50.00 1 $5.00 2
Questions:
1. In which year was Crazy Mathematician's money expenditure per week higher?
1973: 30 x $0.50 + 1 x $50.0= $15 + $50 = $65
1993: 27 x $2.00 + 2 x $5.00 = $54 + $10 = $64
He spent fewer dollars in 1993, more in 1973. Answer is 1973.
2. In which year was Crazy Mathematician's real expenditure higher?
This depend what you mean by "real." If we ask what his 1993 consumption would have cost at 1973 prices, we find
1993 cons at 1973 prices: 27 x $0.50 + 2 x $50.00 = $13.50 + $100 = $113.50; what he consumed in 1993 would have cost much more than what he consumed in 1973 at 1973 prices, suggesting his real consumption has increased.
But if we ask what his 1973 consumption would have cost at 1993 prices, we find
1973 cons at 1993 prices: 30 x $2.00 + 1 x $5 = $60 + $5 = $65; i.e. what he consumed in 1973 he could have still consumed in 1993 for the same number of dollars.
What can we conclude? He actually spends fewer dollars in 1993; he could have bought the same basket of goods in 1993 as he did in 1973 for the same number of dollars [but he chose to buy a different basket of goods, which cost him less]; and what he actually bought in 1993 would have cost more dollars than he spent if he had had to pay 1973 prices. Taken together, this suggests that probably he was better off in 1993 than in 1973, so if "real" means anything sensible we would say his real expenditure was higher in 1993.
3. If we add the information that the consumer price index increased from 100 in 1973 to 330 in 1993, would that change your answer to 2.?
Again, depends what you mean by "real." If we choose to deflate his expenditure by the consumer price index, then he clearly had much lower real expenditure in 1993 [$64/3.3 = about $19.39 in "1973 dollars," deflating the way we normally do – "money" divided by price index times 100 equals "real."] The point here is to make you realize that notions of "real" are averages that do not necessarily reflect the actual experience of people – the standard procedures deflate according to the changes in prices of a very broad range of goods and services [corresponding to the average consumption expenditure of all households]. What any particular person or household actually buys may be quite different, so what the standard procedure says about their real income or expenditure may not match whether they actually are better off or not – "Crazy Mathematician" in this example is probably better off in 1993, although the standard procedure suggests his real expenditure is much lower.
4. For 2. and 3., why? Do we have any basis for knowing whether Crazy Mathematician was better off in 1973 or 1993, other than knowing what he might tell us?
Typically, the answer is no. The particular numbers here are set up to strongly suggest he was better off in 1993, but in general if we are talking about individuals the standard calculation of what has happened to "real" income or "real consumption expenditure" does NOT tell us that individual is better or worse off – only that on average over large numbers of people, that would be so. This is because what people actually buy does not match the basket of goods in the base of the price index, AND they change what they buy when relative prices change. The latter point gives rise to what is known as the INDEX NUMBER PROBLEM – that if the basket changes, that means the weights in the index should change, but then one does not know what the "right" basket or weights to use for the index are. This problem is insurmountable in a true sense; what we do is make approximate compromises. For the CPI, we use a fixed basket and revise it every ten years or so; for GDP, we use a chain index – linking each pair of adjacent years, but changing the weights every year.