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There is a standard reason why real GDP growth is defined the way it is: it works locally in time and that’s really the best you can ask for from this kind of measure. If you have an agent with utility function u:Rn→R defined over n goods with no explicit time dependence, you can express the derivative of utility with respect to time as
du(c1,c2,…,cn)dt=n∑k=1∂u∂ckdckdtIf you divide both sides by the marginal utility of some good taken as the numeraire, say the first one, then you get
du/dt∂u/∂c1=n∑k=1pckdckdtwhere pck is the price of good k in terms of good 1. The right hand side is essentially change in real GDP, while the left hand side measures the rate of change of utility over time in “marginal units of c1”. If we knew that the marginal utility of the numeraire were somehow constant, then changes in real GDP would be exactly proportional to changes in utility, but in general we can’t know anything like this because from prices we can only really tell the utility function up to a monotonic transformation. This means real GDP is by construction unable to tell us the answer to a question like “how much has life improved since 1960″ without some further assumptions about u, since the only information about preferences incorporated into it are prices, so by construction it is incapable of distinguishing utility functions in the same equivalence class under composition by a monotonic transformation.
However, real GDP does tell you the correct thing to look at locally in time: if the time interval is relatively short so that this first order approximation is valid and the marginal utility of the numeraire is roughly constant, it tells you that the changes over that time period have improved welfare as much as some extra amount of the numeraire good would have. If you want to recover global information from that, real GDP satisfies
1RGDPd(RGDP)dt=du/dtNGDP×(∂u/∂c1)so what you need for real GDP growth to be a good measure of welfare is for nominal GDP (GDP in units of the numeraire) times the marginal utility of the numeraire to only be a function of u, which I think is equivalent to u being Cobb-Douglas up to monotonic transformation. The special nature of Cobb-Douglas also came up in another comment, but this is how it comes up here.
I think the discussion in the post is somewhat misleading. There’s really no problem that real GDP ignores goods whose price has been cut by a factor of trillion; in the toy example I gave with Cobb-Douglas utility real GDP is actually a perfect measure of welfare no matter which goods have their prices cut by how much. The problem with real GDP is that it can only work as a measure on the margin because it only uses marginal information (prices), so it’s insensitive to overall transformations of the utility function which don’t affect anything marginal.
Curious to see what people have to say about this way of looking at the issue.