Wednesday, July 21, 2010

A Brief Keynesian Digression

This will help with the next posting. Its not necessary, but if you don’t understand it you will have to take some things on faith.

Over the long run, Consumption and Income (or production) are equal, for economies of all sizes. Everything that is consumed must first be produced. Everything that is produced is pretty quickly consumed. Yes, there are inventories, but they are seldom for more than a few months, and they usually stay more or less stay the same. (Every economy, especially modern ones, is at most, only a few months from disaster) Let’s draw a picture, Diagram 1, with Consumption on the vertical axis and Income on the horizontal axis. Then the line where they are equal, for economies of all sizes, is the 45 degree diagonal. If we draw a point above this 45 degree diagonal, the economy it represents will have Consumption greater than Income. Below this line, Income is greater than Consumption. So any economy we talk about, is in the long run, going to be a point on this 45 degree diagonal. If we talk about a 100 billion economy a, it will lie on this line, where its Income and its Consumption are equal. The same for a 200 billion economy b, or a 500 billion economy c.

Now think about Consumption. If our economy is really little, we are going to want to consume more than we produce. If our economy is bigger, we are going to produce more than we want to consume. (Then we are also going to want to save, or more properly accumulate.) We represent what we want to consume by a line C. Diagram 2. This line is called a curve, by economists, lest they forget, as they sometimes do, that it really doesn’t have to be straight. The distance between this line, and the bottom of the graph, is how much we want to consume, at each level of income y. It slopes upward because the greater people’s income (y), the more they want to

Consume. Now this line C, this curve, crosses our 45 degree diagonal, at point e. Below, to the left of this at point e’’ for instance, our economy is little, and people are going to want to consume more than they produce. (In this simple model they can’t, of course. They have to starve) So the Consumption line is above the 45 degree diagonal, more desire to consume than income. To the right of e, at e’ say, our economy is larger, and people are going to have leftovers from what they want to consume, which they will want to save. As our economy grows bigger, and moves further to the right of e, people will want to save more and more. This is shown by the vertical distance between the 45 degree line, and the Consumption line C. Note they are also consuming more and more.

Now this Consumption line is sort of a matter of attitude. (And other things. In fact, this whole argument, is a matter of attitude. As is the diagram, except for the fact that the economy is on the 45 degree diagonal. Notice we’re also ignoring little things like taxes and government and exports and imports.) If people feel like consuming a greater proportion of their income, for a given size of their income, the Consumption line would be higher. This is shown by curve C’ in Diagram 3. At the size of income marked by y, though people are neither saving or dissaving at C, at C’ they want to consume so much they would be dissaving.

Back to the C curve, and Diagram 4. At income y, C is below the 45 degree diagonal, and the difference is how much the people in the economy want to save. (Want to consume + want to save = what is produced.) Now, where can this savings go? It has to go somewhere, because in the long run, economies cannot accumulate stuff. Economies do not save. (This is particularly true of market economies. A company that ‘saves’ too much of its product ends up going under. Well, maybe except for banks. But saving money is not saving stuff.) Nobody is going to make 50 million dishwashers, or 50 million cars, so that 5 or 10 years down the road, they will have them to sell. (Inventories that are accumulated are for at most a few months, and we’re talking about longer than that. Also, note that services cannot be saved.) No. They’re going to want to build a factory to make these things. They’re going to want to invest in a factory. That’s where all the savings goes, investment, and so savings is equal to Investment. (Remember, we’re talking about real savings. Right now, people are money savings like crazy, or trying to. But it is not being invested. So really, they are not saving anything. THey are redistributing demand, both in the present, and the future.)

Now Investment uses resources and is therefore like Consumption. Desired Investment also depends on the Income of the economy, so it can also be represented by a curve, and if we take this curve for desired Investment and add it to the (desired) Consumption curve, we end up with a total, the sum of Consumption and Investment, which economists call Aggregate Expenditures, or AE curve. Actually, what we have here is Aggregate desired Expenditures. Now where wishes, that is the AE curve, meet with reality, that is with income, or production,(y) on the 45 degree line, at e, we have the size of the real economy. This is also where desired savings is equal to desired investment. (We cheated and used a different argument, that real investment and real savings really have to be the same. The Keynesian argument with desired savings and desired investment is more complicated: Suppose the economy produced more than at e, at e’ say. Then the economy would be really producing more than people wanted to expend (at the AE curve.) So with all this extra production, inventories will expand, producers will want to cut back, they will invest less, and the economy will fall back to e. Suppose instead, the economy produced less than at e, at e’’, say. Then the economy will really be producing less than what people want to expend. Inventories will shrink, producers will see this and want to produce more, so they will invest more, and the economy will grow, back to e.)

Now this diagram doesn’t explain very well how economies grow, and move up the 45 degree line as both income, that is production, and consumption grow. Apparently, the AE curve has to keep shifting upward, which means either desire to Consume, or desire to Investment, or both must also keep shifting upward.

In the diagram, though, the economy is kind of stuck at e, because we can’t save more than we invest, and we can’t invest more than we save.

From this diagram, we can draw a simpler diagram of just the relationship between desired Savings and desired Investment. We do this by simply subtracting the Consumption curve in the diagram. If we subtract the C curve, that is shift the C curve down to the horizontal axis (down the orange arrow) and keep the other lines in the same relationship to each other, we have a diagram of the relation between desired savings and desired investment. Diagram 5.

As in Diagram 4, the economy we are talking about is really where the lines cross, at e, where desired Savings equals desired Investment. This is the diagram we will be discussing in the next posting.

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