Saving = Investment, the Classical Equilibrium Condition: A Clarification

This quick post is a follow-up from my previous post, Basic Classical Model. Those of you who’ve read that post, will recall that the Classical Model of macroeconomic theory asserts that an economy tends to move towards “full employment” on its own (Full employment refers to the situation when the labour market is in equilibrium i.e. demand for labour = supply of labour at the existing wage).

At the full employment level, output will be = spending for the economy as a whole. This belief is rooted in Say’s law, which asserts that supply creates its own demand. 

Here’s the basic National Income Accounting (NIA) identity that we’ve all learnt at school, which is based on the same general idea. 

Y (output) = C + G + I (total spending) 

where Y = output, C = consumption spending, G = government spending and I = investment 

But what really ensures that this identity holds? (I’ve discussed this in my post: Basic Classical Model) 

According to the Classical model, the flexible interest rate in the loanable funds market adjusts to ensure that the demand for funds is equal to the supply of funds, so that Output = Spending for the economy as a whole. 

Different textbooks lay down this condition in slightly different ways, which can cause confusion. I hope to erase that confusion in this post. 

Let’s define a few terms first

Y = C + I + G

Y - C - G = I (re-arranging the NIA identity)

Now, Y - C - G = S (National Saving)            (1)

This makes sense. From total output (Y), if we subtract total consumption expenditure, both private (C) and government (G), we’re left with savings for the whole economy.

Subtracting and adding T (net taxes) on the LHS of eq. (1) gives us:

(Y - T - C) + (T - G) = S 

Where (Y - T - C) = Private Saving and (T - G) = Public Saving            (2) 

Private Savings are the savings of households. From total income (Y), once we subtract taxes (T), we get the disposable income of households. This disposable income (Y - T) is either consumed or saved. Hence, Y - T - C = the savings of households. 

Public Savings (the savings of the government) are = government revenues - government spending = T - G. 

With that background, let’s derive the condition for equilibrium in the loanable funds market.

How Mankiw (Macroeconomics, 5th edition) describes the condition for equilibrium in the loanable funds market

Mankiw assumes that the supply of funds = National Savings (S) 

and the demand for funds = Investment (I). 

The loanable funds market is in equilibrium when National Savings are = Investment (S = I). 

This condition is easily derived from the NIA identity. 

Y = C + I + G

Y - C - G = I

The LHS of the above equation = National Savings (refer to eq. 1), which implies that S = I.

This manipulation of the NIA identity shows us that when National Savings = Investment spending, the loanable funds market is in equilibrium, and output = spending. 

How Hall and Lieberman (Macroeconomics: Principles and Applications) describe the condition for equilibrium in the loanable funds market

They assume that the supply of funds = Private Savings (PS)
and the demand for funds = Investment (I) + budget deficit (G -T)

When the interest rate adjusts so that PS = I + G - T, the loanable funds market is in equilibrium, and output is = Spending.

Let’s prove this. We start with the NIA identity. 

Y = C + I + G

Subtracting T from both sides of the eq. and moving C over to the LHS gives us:

Y - T - C = I + G - T 

Remember, Private Saving = Y - T - C (see (2) above) 

So, the eq. above implies that PS = I + (G - T)

Hence proved. Simple, isn't it?

Conclusion

Both S (National Savings) = I, and PS (Private Savings) = I + G - T, are the same condition. Both are a manipulation of the National Income Identity (output = spending).