A Basic Macroeconomic Equation System from Arnold Kling

Short form: A Basic Macroeconomic Equation System

Long form: Introduction to Macroeconomics

The long form includes the short form. But I'm starting with the short one.

The model is pretty simple. As Kling points out, "There is no government or foreign trade sector." So it is only a place to start. But that's okay.

The file is undated. But Kling's example uses the value $8.5 trillion for GDP. That's about what our GDP was in 1997. Maybe the file is from that era.

Hey, I worked thru it and maybe I learned something. The last part of Kling's file is "The Paradox of Thrift". I worked it out in the model, in Excel. I answered Kling's questions:

What happens if people try to save more? In particular, what happens if the marginal propensity to consume falls ...?

The result surprised me. Income falls, but saving does not change. Total income goes down, and saving becomes a larger portion of it. If ... if deflation lowered prices along with incomes, the real value of saving would rise. That would invalidate the paradox. I have never seen this result in any of the "paradox of thrift" stories I've read.

I get it now! As Kling says: "in our simple model, business investment (I) is exogenous." Yeah, it's just a number typed into a spreadsheet cell. It's not calculated. So investment cannot change in Kling's Short Form model. And saving equals investment. So -- in the model -- saving cannot change.

This doesn't mean that the Paradox of Thrift is wrong. It only means that the model cannot show us what happens.

Come to think of it, maybe that was Arnold Kling's point. The first equation he gives us is a simplified version of Y=C+I+G+NX. The only other equation in the model is a calculation for consumption expenditures, the "C" in the first equation. There is no equation for the "I" in that equation, business investment.

Investment is a constant in the model. Therefore, saving is a constant in the model.

Kling says, "For most of the rest of this section of the course, we will be adding variables and equations to the macroeconomic model." Then immediately he goes to the Paradox of Thrift, which cannot possibly work unless the model has more variables and more equations.

Good job, Arnold. You made me think.


// My Excel file