I won’t bother to explain the context: Murphy, Krugman, etc.

If you care, you already know the context with p = 0.87.  Bob Murphy writes:

Cowen is right that a sustainable lengthening of the capital structure initially requires a reduction in consumption; what happens is investors abstain and plow their savings into the new projects. But during a central-bank-induced boom, there hasn't been real savings to fund the new investments. That's why the boom is unsustainable, but it also explains why consumption increases at the same time. It's true that this is impossible in the long run, but in the short run it is possible to increase investment in new projects, and to increase consumption at the same time. What you do is neglect maintenance on critical intermediate goods, just as our islanders were able to pull off the feat for a few months.

Krugman's response, which focuses on slightly different issues, is here.  I will say that in the Austrian theory, once the central bank lowers the real interest rate, the increase in investment ought to come from shorter-term processes, such as real consumption.  (That's if you think the interest rate substitution effect is dominant, as the theory implies.)  Capital maintenance is usually a longer-term process and it ought to be encouraged by the lower rates induced by monetary policy.  The employment and liquidity boosts of the boom also might encourage more capital maintenance.

There is of course a literature on the cyclicality of depreciation, capital maintenance, and so on.  Overall it supports my claims, for instance: "In all cases, investment and maintenance are gross complements."  Or see here.  The most careful study I could find, based on Canadian data, shows that investment and capital maintenance move together in the same direction.  This piece argues for countercyclical maintenance expenditures, but not on the basis of any actual evidence.  In any case, how much is capital maintenance as a percent of gdp anyway?  Here is one earlier Canadian estimate of about six percent.  Will variations in that sum — with conversion time — be enough to support a consumption boom?  With expanding capital investment, a full employment assumption, and a basic closed economy model?  I doubt it.

Maybe Murphy has a revisionist view of the capital maintenance literature or maybe he would consider those unfair tests, because they are not all embedded in Austrian scenarios.  Still, the burden of proof here is on him and I don't see that he has cited evidence at all.  Comovement remains an embarassing empirical fact for Austrian accounts of the boom.