Two Price-setting Monopolists Meet in the Street

Two price-setting monopolists meet in the street. One says to the other:

"I will buy 10 more of your overpriced bananas, but only if you buy 10 more of my overpriced apples in return. Deal?"

The second monopolist accepts the deal.

They meet in the street again the following day. One says to the other:

"Instead of me buying those 10 more overpriced bananas today, could I just lend you those 10 more overpriced apples, at the central bank's newly announced overpriced rate of interest, and you can repay the loan next year? Deal?"

The second monopolist refuses this second deal. So both go back to the first deal.

This is basic microeconomics. If a deal makes both parties better off, the deal happens. If a deal makes one of the parties worse off, it doesn't happen.

The first deal makes both monopolists better off (assuming the apple grower likes consuming bananas, and the banana grower likes consuming apples). Because profit-maximising monopolists set Price above Marginal Cost. So the Marginal Benefit of consuming an extra apple exceeds the Marginal Cost of producing it. And the same for bananas. The apple producer doesn't much want to buy an extra banana at the existing price, since his Marginal Benefit from consuming an extra banana equals the price he pays. But he really wants the banana producer to buy an extra apple at the existing price, since the price he gets exceeds his Marginal Cost of producing it. So he gains more from selling 10 more overpriced apples than he loses from buying 10 more overpriced bananas. Same for the banana producer. So the first deal happens. They can even get to the competitive equilibrium this way, even though both apples and bananas are overpriced, if everything is symmetric.

The second deal makes the first monopolist better off, but the second monopolist worse off. Because the central bank has set the rate of interest too high. At the old interest rate, neither wanted to borrow or lend to the other, by assumption. At the new higher rate of interest, each wants to lend to the other, but neither wants to borrow. So the second deal doesn't happen. (OK, they could do a third deal, where one agrees to borrow from the other in exchange for the other borrowing from him, but that third deal is just a wash: it's equivalent to the first deal). If the two monopolists are identical in their preferences for borrowing or lending, there will be no borrowing or lending between them, regardless of the rate of interest. The rate of interest is irrelevant; just like any price is irrelevant, for two identical individuals, who can't gain from trade anyway.

What happens when we introduce a third price-setting monopolist into the story? Now it gets more complicated. It all depends on who likes eating which fruit.

Suppose the apple producer likes eating bananas; the banana producer likes eating cherries; and the cherry producer likes eating apples. We have Wicksell's triangle, with no "double coincidence of wants". That first deal can't happen, unless all three price-setting monopolists meet in the street, at the same time and same place, and agree to a three-way deal. And that's much less likely to happen. And even if it did happen, it's harder to agree to a deal when three people must agree than when only two people must agree.

And that same Wicksellian triangle, which makes it hard for three price-setting monopolists to do the first deal, is also a very traditional economists' story for why people use a medium of exchange ("money"). Money lets them replace one three-person deal with three two-person deals. And that same story is even more compelling if we go from a 3-sided triangle to an n-sided polygon. Money lets them replace one n-person deal with n two-person deals.

And introducing money as medium of exchange into our story puts a totally new perspective on the second deal, where each price-setting monopolist wanted to lend to the other, but the deal didn't happen, because neither wanted to borrow. If you save part of your income by lending it to another person, you need that other person's consent to the deal. But if you save part of your income by simply not spending part of the money you earn, you don't need anyone else's consent. You just spend less money. Done. But if everyone spends less money, then everyone's money income falls too, so the attempts to save by accumulating money work for each but fail for all. The same amount of money just circulates more slowly. We get a recession. And if the n price-setting monopolists in my story had chequing accounts at the central bank, and used those chequing accounts to buy and sell everything else, and if the central bank set the interest rate paid on chequing account balances too high, so everyone wanted to accumulate money, we would indeed get a recession.

[You can read this as a critique, or as a reformulation/reinterpretation, of the canonical New Keynesian model, with its n identical price-setting monopolists, no Wicksellian triangles, with "money" used as unit of account but not, supposedly, as medium of exchange. The model's conclusions (monopoly power makes output too low, setting the rate of interest too high causes recessions) make no sense unless you introduce Wicksellian triangles and a medium of exchange.]

Comments

[marcus nunes]

"If the two monopolists are identical in their preferences for borrowing or lending, there will be no borrowing or lending between them, regardless of the rate of interest. The rate of interest is irrelevant; just like any price is irrelevant, for two identical individuals, who can't gain from trade anyway."
Nick, in his recent Mercatus paper, Covid19 & Fed Monetary Policy, Robert Hetzel writes:"...quantity theorists need to explain why monetary stability requires control of money creation even in a monetary regime of interest rate targeting."
From MV=Py, "...In the traditional exposition, money creation arises independently of the other variables and forces changes in dollar expenditures..."
Now, if money changes arise not "independently" but to offset changes in velocity, intereest rate targeting is also irrelevant. If it´s "too high", the fall in velocity will be offset by a rise in money supply, keeping NGDP growth stable...

[Frances Woolley]

Nick, this makes total sense to me, but I have a question about this bit: "You just spend less money. Done. But if everyone spends less money, then everyone's money income falls too, so the attempts to save by accumulating money work for each but fail for all."

Since I=S, won't capital hungry investor swoop in, take all of the savings, use them to build a road or a factory or a house or a new technology, and kick start the economy with investment spending?

[Nick Rowe]

Marcus: there's the interest rate paid for holding money,rm, and there's the interest rate paid for holding bonds (loans), rb. In my story, rb is irrelevant, because nobody ever borrows or lends (they have identical time preference etc.) But rm matters, because they all hold money. In this case, the central bank is holding the stock of money constant, and raising rm, which increases the demand for money.

Frances: I'm so pleased it all makes sense! There's no investment in the simplest New Keynesian model I'm critiquing here. So actual saving must be zero too. They don't actually succeed in increasing their saving. If we did introduce investment, then if interest rates rise, households would want to lend more to firms to invest, but firms would want to borrow less from households. So actual investment and saving would fall, because you can't force investors to borrow.