I have been teaching basic Keynesian economics this week to my undergraduate class and I have just completed a new book manuscript with the working title of Prosperity for All, that will be coming soon to a book store near you. I am thus highly attuned to the debate over the connection between savings and investment. That debate resurfaced with a vengeance this morning on Twitter when Noah Smith and Jo Michell, among others, engaged in a sometimes testy exchange on the role of the State in promoting investment. Since that debate is at the core of Keynesian economics, and since my class is prepping for Monday’s midterm, this seems like a great opportunity to enlighten readers of all varieties on what Jo and Noah were on about.
Keynesian economics begins with a basic definition. To sharpen the discussion, I will abstract from the role of government and I will abstract from foreign trade. In an economy with no government, and no foreign trade, we may define all of the goods produced in the economy to be of two types; a consumption good or an investment good. Since all of the income earned by the factors of production is earned from producing either consumption goods or investment goods, it is IDENTICALLY TRUE that:
1) YN = CN + IN
Here, YN is the dollar value of all of the incomes earned by workers, capitalists and landowners in the process of producing consumption goods worth CN dollars and investment goods worth IN dollars. The letter N stands for “nominal”.
In recent discourse, economists have sometimes resorted to the fiction of the one good representative consumer model in which we assume that the economy produces a single good from capital and labor. That IS NOT what I am assuming here. YN IS NOT a single good. It is the dollar value of all final goods produced in a given year.
To move from nominal values, to real values, we need to deflate equation (1) by a nominal index. The Keynes of the General Theory made a very sensible suggestion that has been ignored for the past eighty years and that I resuscitated in my book, Expectations Employment and Prices. He suggested dividing both sides of identity (1) by a measure of the money wage. That is a great way to normalize measurements over time because the money wage grows for two reasons. It grows when there is inflation in the dollar. And it grows when there is real economic progress. Dividing equation (1) by the money wage leads to the following identity where Y, C and I represent GDP, consumption and investment measured in wage units.
2) Y = C + I
Equation (2) is, at this point, still an identity. Now comes the economics. Keynes introduced two simple pieces: A theory of aggregate supply. And a theory of aggregate demand.
The Keynesian theory of aggregate supply asserts that firms will increase or decrease the number of workers they employ in order to produce as many goods as are demanded. The French Economist John Baptiste Say, famously asserted that: Supply creates its own demand. Keynes turned this proposition on its head. In Keynesian economics: Demand creates its own supply.
Keynes argued that the economy is typically producing at less than full employment. And as long as there is any involuntary unemployment: everything that is demanded will be supplied. That central proposition can be represented by a graph in which expenditure appears on the vertical axis, and income appears on the horizontal axis. A line at 45 degrees to the origin, for which income equals expenditure, IS the Keynesian aggregate supply curve.
Keynes did not explain why firms would respond to deficient demand by reducing employment, as opposed to cutting wages. He thought that workers would resist reductions in their wages, but he did not believe that sticky wages were central to his argument. Although Keynes never provided a fully articulated theory that would reconcile his ideas with microeconomics: I have provided such a theory. In my published research, I explain why the forty five degree line is an aggregate supply curve. My work is grounded in the microeconomics theory of search. But I digress. More on aggregate supply in a future post.
Recall that my purpose here, is to explain the debate between Noah and Jo on the equality of savings and investment. In order to move forward with that purpose, let us accept, for now, the Keynesian theory of aggregate supply and move to the Keynesian theory of aggregate demand.
Keynes asked, what determines expenditure on consumption and investment goods? He claimed that aggregate expenditure on consumption goods, by a community of people, will increase when the income of the community increases. But it will increase less than proportionally. He called the constant of proportionality, the marginal propensity to consume. We may represent that idea by equation (3):
3) C = a + bY
Here, ‘a’ is a constant that I will call autonomous consumption expenditure and ‘b’ is the marginal propensity to consume.
Finally, we need a theory of investment. Investment, in the basic version of Keynesian theory, is a highly unstable variable that is driven by the animal spirits of investors. Each year, investors make plans and they enact those plans by placing orders for new machines and factories. I will represent the planned expenditures of investors with the symbol IP. Let me also use the symbol X to represent total expenditure and XP to represent planned expenditure. That leads to the following equations,
4) X = C + I
5) XP = C + IP
and, using the theory of consumption from (3)
6) X = (a+I) + bY
7) XP = (a+IP) + bY
Equations (6) and (7) distinguish expenditure, X, from planned expenditure, XP. It is identically true that
8) X = Y
But it is only true, in equilibrium, that
9) XP = Y
The difference between I and IP is that goods that are produced, but not sold, are DEFINED to be investment goods. If Toyota builds 100,000 cars, but only 20,000 are sold, the 80,000 unsold cars are defined to be investment expenditure. But they are not defined to be part of planned investment expenditure. An economy in which unplanned inventories increase by the real value of 80,000 cars is not in equilibrium. To restore equilibrium, Keynes argued that Toyota will fire workers, those workers will spend less, and income will fall to the point where saving equals planned investment.
What about the equality of savings and investment? By definition, every dollar not spent, is saved.
10) S = Y – C
Here, S represents savings. A little further algebra establishes that, when Y = XP, it is simultaneously true that
11) S = IP
Here, finally, is the answer to the exchange between Jo and Noah. It is always true, in equilibrium, that savings is equal to investment. In Keynesian theory, it is income and employment that adjust to make this so. In Keynesian economics: Demand creates its own supply.