## Who pays the price / if you want more

18 March 2009

In economics, when we write or speak of the incidence of a cost or of a benefit, we refer to the ultimate distribution.

Most people get the idea that, often, costs or benefits can be passed along, so that the party upon whom they formally fall isn't necessarily the final recipient. This is certainly true of taxes.

There's a standard result of microëconomics that, if one sets aside the effects of transactions cost (dat ol' debbil), then the incidence of a per-unit tax is same, regardless of whether it is formally placed on the seller or formally placed upon the buyer. Almost every first-term microëconomics course demostrates this result, although they usually dumb-it-down by failing to note that transactions costs can somewhat undermine the equivalence.

The argument goes as follows: Imagine that the quantity offered for sale fits some function S(Ps) where Ps is the price received by the seller, and that quantity that buyers seek fits some function D(Pb) where Pb is the price that buyers must pay. If the pre-tax price is just P, and sellers have to pay additional tax and tax-related costs of ts, and buyers have to pay tax and tax-related costs of tb, then

Ps = P - ts
(tax-related cost subtracted because it is a reduction in the price that what the seller receives) and
Pb = P + tb
(tax-related cost added because it is an increase in how much the buyer must pay). Algebraïcally,
Pb = Ps + ts + tb
and
Ps = Pb - tb - ts
And the market would equilibrate where
S(Ps) = D(Pb)
(At a lower P, D would be greater than S, and it would be in the interest of sellers to increase their prices or of buyers to offer a little more per unit; and, a higher P, S would be greater than D, and it would be in the interest of sellers to cut their prices a bit, or for potential buyers to cut the amount that they offered.) Which is to say that the equilibrium is
S(Ps) = D(Ps + ts + tb)
as if the buyer formally paid all the tax on the seller's received price, and
S(Pb - tb - ts) = D(Pb)
as if the seller formally paid all the tax on the buyer's paid price.

(The next time that you hear or read of a politician arguing for employer-provided benefits, such as for health-care, consider the incidence.)

Now, let's consider the incidence of a tax on carbon emissions (ignoring the question of whether there should be such a tax), in the absense of transactions costs, the incidence would be the same whether the state formally taxed the producer of the emissions, or taxed the consumer of each product associated with the emissions, based upon the amount of the emission associated with that product. But it is plainly less costly to place the formal tax on the producer than to have separate filings for each consumer.

Which brings me to this story:

China seeks export carbon relief from the BBC
China has proposed that importers of Chinese-made goods should be responsible for the carbon dioxide emitted during their manufacture.
Whatever measures are imposed to curtail carbon emissions, they can be conceptualized as a tax. And it's really, folks, not that the Chinese officials don't understand that the incidence would be the same (or very nearly the same) in the absence of transactions costs, nor that they don't recognize that the transactions costs would be lower if the tax were formally imposed upon producers. Rather, it's that the Chinese state
• knows that some consuming nations would avoid or evade the tax, lowering the incidence upon China,
• would be able to disguise some of its emissions for domestically consumed production as emissions for exported product, and
• would like to misdirect blame for any failure to reach agreement.

### 4 Responses to Who pays the price / if you want more

• gringo says:

I've been enjoying your weblog for some time now, I find many of your observations interesting and well-thought out. I am in a constant argument with a friend of mine over the economy and what should be done to fix it - neither of us are economists, which obviously leads us to reach horribly different conclusions.

I have made two observations, based on empirical data and my interpretations of other factors, I would love to hear what your take is on this. First, I believe that as of a week ago, the recession in the U.S. has hit bottom. Second, I would expect that any day now, the Fed will want to begin to increase the Prime Rate. My friend disagrees on both counts.

I will trust your opinion, and pass it on to him, whether I'm right or wrong. Thanks, in advance.

• Daniel says:

Okay, well, I'm going to respond out-of-order.

A Quibble: What the Fed sets directly is the Discount Rate, and it can have a fairly immediate effect on the fed funds rate (by controlling reserve requirements). The prime rate is set downstream from the Fed.

Setting politics aside, the Fed would indeed increase the Discount Rate and perhaps adjust reserve requirements if it decided that the recession had bottomed-out, because the Fed's concerns would then turn to price inflation.

However, I'm not sure whether the Fed is prepared to set politics aside. They would come under attack from those who didn't share their surmise (or sought to play on the fears of others), and the attacks would worsen if the surmise indeed proved incorrect. The Fed may act to save face and/or try to preserve its independence by delaying the fight against price inflation.

And the Fed would indeed be working on surmise. There's a significant lag between when an economy bottoms-out and when we know that it had.

Returning to the issue of politics, I cannot answer what I take to be your principal question, because I just don't understand the politics well enough to know what the Fed, Administration, and Congress are going to do next. A claim that the economy has hit some sort of bottom is at least plausible, but the political system can always do things that will worsen things (often in the guise of helping). I don't even know how much of Obama's budget to expect to pass, and the outcome is going to have a profound effect.

• gringo says:

Great points. The prime rate is set downstream from the Fed. Should it be? The reactive nature of the Federal Reserve has bothered me for years, through many administrations. Maybe it should work this way, or else maybe I'm just a huge fan of Hamilton. I'm sort of torn, because I value a weak central government, but I seem to want strong central control in the banking industry. I'm conflicted.

And I agree, however misinformed that I probably am, that politics have more to do with economics than economics has to do with politics. In other words, I have always felt that both sides have taken great liberties with their advantages in times of economic crises. You have pointed this out in your weblog, bravely and with supportive evidence.

I suppose then, that my question should be more pointed: Pretending that politics are not part of economic recovery, is it wrong of me to suggest that the Fed might want to become proactive rather than reactive? I realize that inflation is defined more relatively these days, as opposed to when I grew up. But still, I have no choice but to point out that the U.S. has suddenly pumped billions of dollars into their infastructure without so much as a wooden nickle behind it (not an Austrian-minded observation, simply an honest one), and I would think that a bump up in the prime rate might be in order as a prophylactic against probable monetary inflation (which, as you point out, is immediately followed by price inlfation).

And my claim that the recession has hit bottom is also empirical. The markets are now happy and the housing sector shows promise, and while I am quite sure that unemployment and manufacturing will continue to decline as they normally do right up until the last point of recovery, I am encouraged by what I am reading.

Again, thanks for your thoughts and I look forward to your response.

P.S: Also, I gage some of my opinion based on the dollar versus the Peso. Right or wrong?

• Daniel says:

Ultimately, interest rates correspond to a price, that of money delivered in the present in terms of money delivered in the future (with the actual price of course being 1 + r, rather than r itself). As with any other price, we want it to incorporate as much relevant knowledge as possible, which calls for using a market process rather than an administrative process. (I believe that, rather than administrating interest rates as such, the Fed — so long as there is a Fed — should focus on M0, slowing its growth in the face of price inflation, and increasing its growth in the face of price deflation.)

In the long run, I'd like to see money quite denationalized. Unlike the typical proponent of denationalization, I do not think that money backed by a single, unchanging commodity is ideal, nor do I think that it would persist in a free market. Rather, I think that issuers should and would issue notes redeemable in multi-commodity baskets, which changed from term-to-term, with terms over-lapping. The issuers whose notes best held over-all value would be most successful, and their notes would be most used.

I don't think that it's at all unreasonable to suggest that, in some sense, the best short-run policy of the Fed would be to push-up interest rates (by various means) in order to choke-off a price-inflation before it sets-in. I believe that the underlying agreement here between us is in the great importance of price stability.

The evidence that you cite was part of what motivated my claim that your surmise was plausible. But some markets will turn not when the economy over-all has hit bottom, but simply when it is believed that the bottom is being approached. Some parties will buy in advance of an expected recovery in the hope of being positioned to take full advantage of the recovery, and others will become more active to supply the first group.

There's nothing intrinsically foolish in using the relative movement of currencies, including that of the US dollar against the Mexican peso, in forming one's expectations of the economic climate.

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