What I'm writing here is probably less novel than its presentation, but I find this a useful way to think about it. (It will seem a bit technical, but I'm going to use language fairly loosely where I can while preserving the idea.)
Hotelling noted that, in some expected-value sense, the price of oil reserves should increase at the rate of interest in equilibrium. If the market interest rate is lower than the rate of a particular producer — if the producer faces higher borrowing costs (perhaps as a poor credit risk) and/or faces a liquidity constraint — then that producer will want to produce more now (even while producing less later). If a country forms rigid spending plans in anticipation of selling oil at a particular price, lower prices tend to induce exactly those liquidity shocks and credit risks that make money comparatively more urgent to them.
There are two things I'm trying to highlight here: one is that non-perishability and trade-offs through time are crucial to this effect, and I think that gets buried in some formulations of this observation. The other is that this is a "liquidity" issue more than a "solvency" issue, or, more to the point, perhaps, that the increase in production in the face of lower prices doesn't increase the producer's wealth as measured using the "market" interest rate. A patient producer wouldn't respond this way; a producer responds this way only in a context of (implicit or explicit) leverage, or at least the coming due of various dollar-denominated obligations.
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