# Money as Medium of Account

Bank of Canada Governor Mark Carney recently gave a speech on monetary policy, where among other things, he discussed price level and nominal GDP targeting. In that speech, he made the following remark:

In addition, under NGDP-level targeting, the central bank would seek to stabilize the GDP deflator in order to achieve price stability. But the GDP deflator measures the price level of domestically produced goods and services, which may not match up well with the cost of living that the CPI measures and that matters most for welfare, particularly in small, open economies where imports make up a substantial share of the consumption basket.

Contrary to others, such as Scott Sumner, I don’t see this as a ridiculous statement. This post is my attempt to explain why.

To assess Carney’s claim, we need to answer a simple question. What measure of the price level should we want to stabilize? To answer this question, we will think about money purely as a medium of account. In doing so, I can hopefully demonstrate that Carney’s statement is entirely consistent with my argument.

Consider an individual with a utility function, $u(x_{it}), i = 1, \dots, n$, where $x_{it}$ measures the consumption of good i at time t. Now let’s suppose that consumption for this individual is fixed for all future periods, t = t+1, t+2, … We can thus confine our attention to the present decision. Consider changes in $x_{1t}, \dots, x_{nt}$. Some of the changes in the composition of the basket of goods will not affect utility, whereas others will. The individual will choose the composition of his basket by choosing the combination that maximizes utility subject to his budget constraint.

This basic application of consumer choice theory poses what is called an index number problem. Namely, the question is what price or combination of prices has to be held constant in order to prevent resource misallocation due to inflation. In other words, how should we deflate money income in the consumer choice problem when inflation occurs? Put succinctly, the solution is to identify the price index for which real income remains constant as we move along the indifference surface. Another way of saying this is that, for a given indifference surface, it is possible to adjust the price level to maintain constant money income. The absolute price level that corresponds with this condition could be found for every single point along an indifference surface. Thus, it would be optimal for monetary policy to choose the quantity of money to achieve the price level that would maintain constant money income.

So what does this mean in terms of Carney’s comments? Basically, it means that the construction of an appropriate price index should include the prices of goods that are in the individual’s utility function. Thus, for a small open economy, the appropriate price index to target is likely that which includes imports. The GDP deflator might be inappropriate.

This may or may not be a good way to think about monetary policy, but I think that it does demonstrate that Carney’s distinction is grounded in economic theory.

Also, just so Scott is happy, I should note that if the central bank were to target the properly constructed price index, money income would be the appropriate measure of welfare (because money income would be monotonically related to utility).

[For more on the index number problem, see Jurg Niehans's, The Theory of Money. What is presented above is largely a (terse) summary of what I remember discussed in that text.]

**Note: “Money is here called a medium and not, as customary, a unit of account because, clearly, money itself is not a unit, but the good whose unit is used as the unit of account.” (Niehans, 1978, p. 118n)

### 6 responses to “Money as Medium of Account”

1. It seems to me that you are arguing that the goal of monetary policy should be to stabilize a measure of the price level so that changes in money income reflect changes in utility. It is the other side of the coin of finding out how real income has changed when there is inflation.

I am puzzed how we do this when there are many people whose utility surfaces vary.

But be that as it may, I guess I think the purpose of monetary policy is to make sure that changes in money income represent proportional changes in utility.

The GDP deflator, it seems to me, provides better evidence of whether nominal expenditure is consistent with productive capacity. In my view, monetary disequilibrium disturbs this relationship and it should be avoided.

For any open economy, exports are a demand for domestic output and imports are not.

It is true that if the terms of trade deteriorate, then real income falls, and if money income is to move with real income, then money incomes need to fall.

But is that the goal? What people need is a signal that they can’t afford as many foreign goods. Higher prices for them seems like a cleaner signal. Yes, it lowers their real income, and so the unchanged nominal incomes that would result from avoiding excess presure, one way or another, on the GDP deflatlor, fail to reflect the lower real income. So?

While I do rather like the idea that higher nominal income should reflect more utility in some sense, but not of the expense of having lower real income and output.

In particular, forcing nominal incomes down so that they will reflect the reducd utility from higher oil prices seems like a bad idea to me.

2. Josh: you lost me. If money income were constant (more generally, if money income were invariant to the monetary policy target index) then targeting the CPI would presumably maximise E(U(C)). But why would money income be invariant to the policy target index?

3. Bill,

Yes. I didn’t mean to say that this type of policy is desirable, but rather that it is possible that this is what Carney has in mind. If individuals have sufficiently different indifference surfaces, it is impossible to conduct monetary policy in this manner.

Nick,

This is a story about inflation affecting relative prices. If relative prices remain unchanged when there is inflation, any arbitrary price index is sufficient to deflate money income.

I’m not sure if this is what you are looking for, but consider a numerical example. Suppose that there are two goods, milk and bread. Consider two arbitrary points on an indifference curve. On point A, the basket of goods is 3 gallons of milk and 3 loaves of bread. On point B, the basket of goods is 1.5 gallons of milk and 5 loaves of bread. The relative price ratio (given by the tangent budget line) at point A is 1 and the relative price ratio at point B is 2. Now let’s assume that at point A, the price of milk is \$1. This implies that the price of bread is \$1 as well.

The individual is indifferent between point A and point B. Suppose that inflation generates changes in relative prices. The goal is to provide a price index such that real income remains unchanged. In other words, the goal is to keep money expenditure at B a the same level as point A since the individual is indifferent between the two. If we don’t then the individual is moving to a different indifference curve and there are welfare implications.

Thus, if the price of milk is \$1 and the price of bread \$1 at point A, total expenditure is \$6 (given the assumptions above). To maintain that, we know that the price ratio is 2 at point B and the amount consumed. Thus, the new prices of milk and bread are \$1.50 and \$0.75, respectively, at point B.

There exists an absolute price level at every point along the indifference curve. Monetary policy could then, in theory, supply the quantity of money to achieve the appropriate absolute level of prices.

4. Unit of account.

• Lee,

I meant medium of account. See the note that I added to the original post. Money is not a unit of account because money is not a unit.

5. But ‘medium of account’ makes no sense. Accounts don’t need a medium; they need a unit of measure.

I don’t understand your note. Sure, money is a good and not a unit per se, but then the quote continues and explains how a unit of money is normally used as the unit of account. Isn’t that exactly what everyone means when they say money is the unit of account. That’s what I mean. What else could they mean?