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which tends to have a positive effect on the replacement cost of the capital stock and a negative impact on corporate capitalization.

An empirical rather than analytical observation, right?  Since, in principle, inflation can have the same positive effect on the value of different kinds of assets (through an increase in expected future profits); and the rate of interest is universal in its effect on capitalization.

Does a possible explanation lie in differential risk, as corporate capitalization is more susceptible to the heightened “risk environment” of high inflation rates?

Or maybe a simpler (connected) explanation: capital stock pricing is influenced more by debt, and an increase in the price of debt (interest) is transferred to the price of capital stock commodities by its sellers.