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# A Simple Micro/Macro Corona Tax Model

Summary:
I want something you could teach to first or second year economics students. Using tools they already have in their toolkit. MICRO Start with a Demand and Supply model of the market for haircuts. If we put a per haircut tax on buyers of haircuts, the demand curve shifts vertically down by , reducing Q* and P*. If we put a per haircut tax on sellers of haircuts, the supply curve shifts vertically up by , reducing Q* and increasing P*. If we put a tax on both buyers and on sellers of haircuts, both the demand and supply curves shift. We know that Q* falls. We don't know whether P* rises or falls. It depends on which tax is bigger; and it depends on whether demand or supply is more elastic. The coronavirus is like a tax. Every haircut bought and sold comes with an extra cost to

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I want something you could teach to first or second year economics students. Using tools they already have in their toolkit.

MICRO

Start with a Demand and Supply model of the market for haircuts.

If we put a \$1 per haircut tax on buyers of haircuts, the demand curve shifts vertically down by \$1, reducing Q* and P*.

If we put a \$1 per haircut tax on sellers of haircuts, the supply curve shifts vertically up by \$1, reducing Q* and increasing P*.

If we put a tax on both buyers and on sellers of haircuts, both the demand and supply curves shift. We know that Q* falls. We don't know whether P* rises or falls. It depends on which tax is bigger; and it depends on whether demand or supply is more elastic.

The coronavirus is like a tax. Every haircut bought and sold comes with an extra cost to buyer and seller: the buyer risks getting sick; and the seller risks getting sick. (But the "tax revenue" isn't a gain to the government; it just gets thrown away as a net loss to everyone.)

I've drawn the above diagram with a roughly equal "Corona tax" on buyers and on sellers. Because I don't know which is bigger. But I have drawn a demand curve that is more elastic than the supply curve. Because I think that is roughly right, at least for the Short Run. And if demand is more elastic than supply, and the two taxes are the same, then P* falls.

And if the price of haircuts is sticky, and takes time to adjust to the new lower equilibrium price P*, we would see an excess supply of haircuts.

If the Corona tax is big enough, Q* may drop to zero, and the market for haircuts closes down completely.

Even if the Corona tax is not big enough to close down the market, the government might decide to close it down by law. Because the Corona tax also creates a negative externality, because if the buyer or seller gets sick, he or she might also infect other people who aren't buying or selling a haircut. So the Marginal Social Benefit of buying a haircut is less than the Private Marginal Benefit, and the Marginal Social Cost of selling a haircut is greater than the Private Marginal Cost. So the efficient quantity of haircuts Q^ might be zero, even if the market equilibrium quantity Q* is still positive.

Obviously, this will depend on the particular good. It might be efficient to ban the sale of haircuts, but allow people to buy and sell apples. Some markets close, or are closed; other markets stay open.

MACRO

That was Micro. Now lets do Macro, for those markets that do stay open, all lumped together in aggregate. So we are talking about Aggregate Demand and Aggregate Supply.

Eventually (we hope) the risks of buying and selling goods will go away, or at least get smaller. The Corona tax is a temporary tax. We can avoid the tax, by waiting to buy, or waiting to sell, until it goes away (or gets smaller). And the rate of interest is the extra price we pay for buying goods now, rather than waiting till next year; and it's the extra price we get for selling goods now, rather than waiting till next year. (Strictly, it's the real interest rate, which is the nominal interest rate adjusted for inflation.)

So put the real interest rate on the vertical axis, and relabel the curves "AD" and "AS".

Will the equilibrium rate of interest r* rise or fall? In other words, will the Bank of Canada need to raise or lower the rate of interest it sets to keep AD equal to AS (even though both AD and AS are lower than before). In other words, which curve shifts leftwards more, AS or AD?

That depends, on two things: it depends on whether the AD curve shifts vertically down more or less than the AS curve shifts vertically up (is the Corona tax bigger on buyers or on sellers); and it depends on which curve is more elastic (but here we are talking about intertemporal or interest-elasticity -- on how willing buyers and sellers are to postpone buying and selling until next year).

As before, I don't know whether the Corona tax is bigger on buyers or on sellers, so I've drawn it roughly equal. But I've assumed the AD curve is more interest-elastic than the AS curve, so r* falls, and the Bank of Canada needed to cut r. Because that seems plausible to me, and that is what the Bank of Canada actually did.

One big thing this model leaves out is this: buyers of goods expect to be able to buy a much wider variety of different goods (and services) in future than they can buy now. That also shifts the AD curve leftwards for the remaining goods. It's like they learn that they will be able to buy some fancy new device next year, that they can't buy now, and so want to save part of their current income because there are better things to spend their money on next year. See my previous post.

Update 1: A second big thing this model leaves out is that some sellers get hit much worse than others. Unemployed hairdressers might be borrowing constrained, and unable to buy as many apples as they want, because fully-employed apple producers aren't willing to lend to those with a bad credit risk.

[Update 2: I messed up slightly when drawing the two diagrams. If the "tax" on buyers is exactly equal to the "tax" on sellers, the point where the red S curve crosses the blue D curve should be exactly above the point where the blue S curve crosses the red D curve (same Q for both points). Which is the tax incidence irrelevance thing. Oh well