The Economics of Depleting Our Finite Supply of Patriot Missiles

 When I teach undergraduate environmental economics, I ask my students to solve (not using AI), the following problem.

You are an oil monopolist. You see to maximize the present discounted value of your profits this year + next year’s profits. The world ends at the end of next year.

You own 500 gallons of oil. The market interest rate is r%. You can extract your oil for a price of zero.

You take global demand for your oil as given; This year; aggregate demand = 4000 – 10*Price and next year aggregate demand is expected to be; X – 10*Price where X>=4000.

Solve for your optimal extraction of your oil this year and next year as a function of X and r. I am looking for students to figure out that if X is larger then the monopolist chooses to keep the oil in the ground and sell more next year. Conversely, if the interest rate r is higher, the monopolist sells more of the oil now. Opportunity cost if the reason here.

I then introduce insecure property rights. Suppose that the monopolist has guaranteed rights to the oil today but there is an Q% chance that a dictator will nationalize the oil next year. How does the monopolist’s oil extraction path vary as a function of Q? The student should show that the monopolist extracts and sells more oil today when there is a greater chance of confiscation (I.e tax).

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What does this model have to say about the Pentagon’s finite Patriot Missile supply?

As we use up a finite stock of a resource for which we don’t have a close substitute, this shadow price of using it should rise. The Pentagon should be charging itself a higher implicit price for each missile it now uses because it is marching closer to having none at all. If our military has none left, then we face fat tail risk of not being able to protect a key asset.

Let’s return to my algebra above.

Recall that I wrote down next year’s demand for oil = X – 10*Price and X>4000

Suppose that X = 1 million;

Quantity of Oil Demanded next year = 1 million – 10*Price

Suppose there is no oil left in the world; so the left side equals zero

0 = 1 million – 10*price

The oil monopolist could have been paid $100,000 for that gallon of gasoline next year if he had simply not sold all of his inventory this year!

When we run out of a resource, the marginal price for the last unit is very high. This is why the monopolist chooses to save some today in order to sell tomorrow.

The for profit monopolist anticipates this future scarcity incentive and responds to it by engaging in conservation (I.e not consuming today).

Does our Pentagon engage in a similar logic? Or does it reason that the war will end soon?

Now, if our Pentagon embraces this Econ 101 view of rising scarcity ; it will expose our troops and our allies to more risk because we will use fewer of these defensive weapons.

The economics of expected loss arises here;

Our enemy seeks to maximize causing us expected harm; so it targets areas with many people, or valuable capital ; the expected damage caused by an attack =

probability successful attack*$ value of damage if a successful attack occurs +

probability of successful attack*lives lists*value of life

As we have fewer Patriot Missiles, our enemies will launch more attacks because they are more likely to be effective. They will also target asset rich areas to cause more damage to demoralize us.

An unintended consequence of our using our weapons early in this War, is that our enemies will now launch more attacks.