# Why Should Expenditure Equal Income in Computable General Equilibrium (CGE) models?

I'm reading up on CGE models and one clearing condition that must be met is that Expenditure must equal income.

This seems odd to me because I thought households allocate income to savings and expenditure.

• Maybe it is a model without savings, how are we supposed to know? There are very many CGE models, especially since they are widely used around the world by governments that have designed there own special versions. But a simple model would potentially ignore savings. Introducing savings can quickly become very complex because this opens the question of dynamic optimzation unless one simply assumes fixed saving rates. Dec 13 '20 at 15:03
• Thanks! I didn't realize that there were many CGE models, but, yes, that makes sense. I think I'm just confused because in the paper I'm reading the authors write that they assume households allocate income between expenditure and savings but then one of their market clearing conditions states that Expenditure must equal Income. Dec 13 '20 at 15:20
• @JesperHybel no this is actually common condition in most macro models because macroeconomically spending = income even with the presence of saving (since they are investment expenditure)
– 1muflon1
Dec 13 '20 at 16:37
• True my mistake. You are right. Dec 13 '20 at 18:08

It is because saving is investment expenditure, they must be equivalent in standard macro models. To explain this forget about CGE models for a second, they are set up in this way because all macroeconomics is set up in this way.

In macroeconomics by definition income = expenditure. This is definitional. For closed economy by definition income (Y):

$$Y \equiv C+ I + G \tag{1}$$

where $$C$$ is expenditure on consumption (which is what you likely confused with expenditure in general), $$I$$ is expenditure on investment (public plus private saving), and $$G$$ is government expenditure (see more details in Blanchard et al Macroeconomics a European Perspective).

Now $$I$$ will by definition be equal to public and private saving since private saving $$S_p$$ is by definition income not consumed after taxes: $$S_{p} = Y-T-C$$. Public saving $$S_G$$ is by definition any difference between taxes and government spending $$S_G = T-G$$. Together then all saving must be:

$$S= S_p+S_G = Y-T-C+T-G=Y-C-G$$

Now this must be equal to investment since just by rearranging equation 1 we find that investment is:

$$Y-C-G =I \implies S=I$$

Hence the reason why the CGE imposes restriction that income is equal to expenditure is not that there should be no saving (although there might be simplified models where saving will be 'turned off' to make it easier for students). It is because expenditure and income are macroeconomically equivalent even in presence of saving (which is just investment spending).

• Thank you for this well-thought out response! This actually makes more sense. You're correct--I confused expenditure in general with consumption spending in particular. Dec 13 '20 at 17:31
• Consider the Robinson Crusoe economy where one man lives alone in the wilderness or Commonwealth territory. He uses labor to produce a mix of consumption and investment goods. The allocation of labor in production determines the level of investment. There is no financial saving. I don't think it makes sense to say saving equals investment or expenditure equals income in this toy model because there is no money or finance relations. To state that expenditure equals income the classical factors of production are labor, land, and capital. Expenditure equals income as wages, rent, and profit. Dec 14 '20 at 3:10
• @SystemTheory they are by definition equal, as proven mathematically. I think issue here is that since you are not an economist you might be unfamiliar with terminology used in economics. In economics saving does not have the same meaning as saving in common English. In economics saving is by definition difference between income and consumption. This holds even in Robinson Crusoe economy. Investment is only possible if income/output is not immediately consumed, if Robinson Cruse catches 5 fish but eats only 4 in economics that would be saving and that extra fish would be inventory investment
– 1muflon1
Dec 14 '20 at 3:23
• This comment thread isn't really valuable anymore. Can you guys take this somewhere else, please? @1muflon1 is correct. What he has provided is just an economic definition--something learned in introductory economics courses. Please move your debate somewhere else. Dec 15 '20 at 14:12
• @Andrew yes, I wont be discussing this here anymore. I should have ignored the off topic comment and just flagged it as an irrelevant but I always like to presume that people are actually trying to learn here and hence sometimes I let myself get baited into off topic discussions.
– 1muflon1
Dec 15 '20 at 14:17