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I noted in a previous mail that the economics profession as a whole had lost interest in
reswitching (and capital reversal and the like). It may be worth noting that the
profession also (a bit later) lost interest in formal, fully-disaggregated, intertemporal,
general equilibrium theories, probably for much the same reason. On an abstract level one
can show that reswitches may occur in a certain sort of model, just as one can show that
general equilibrium in a certain class of model may or may not exist, be unique and be
stable. But this doesn't seem to yield any useful insights into significant real-world
issues (like: can growth with low inflation continue? Can the US balance of payments
deficit be sustained? Why has inequality increased in many countries? What are the effects
of monetary union in Europe?).
 
There is a case, of course, for working on theoretical issues, but there is a point at
which diminishing returns set in. Something related to reswitching might perhaps cause
important phenomena (market crashes, say). So might non-existent or multiple equilibria,
which we know could occur for reasons which have nothing to do with capital theory (non-
convexities of preferences or technology, say). But that doesn't help, does it, unless you
can do the real work of explaining actual cases and providing robust supporting evidence.
 
Mat Forstater thinks that it is a matter of logical inconsistency, but there is nothing
logically inconsistent about an aggregate production function. Technology might be such
that an aggregate production function is a good approximation, or it might not. The test
is empirical. Similarly, aggregation of labour inputs might work or it might not. It
probably depends on the question asked - homogeneous labour is not going to help explain
widening wage inequality, for example. (Many of those who insist on capital heterogeneity
happily assume homogeneous labour.)
 
Incidentally, reswitching is a particular case of a general result: a discounted cash flow
comparison of two alternative streams of net income can exibit reswitches, that is, the
internal rate of return to the difference between two alternatives can exibit mutiple
roots (up tothe number of sign reversals in the stream of dated differences betweenthe two
streams of cash flows, if memory serves). Hence alternative A may be preferred at high and
low discount rates but not at intermediaterates. They can even switch in and out many
times. That may be the point behind the reference that Mat cites.
 
Tony Brewer 
 
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