# why isnt private sector savings defined as $S=Y-T-C-I$?

why isnt private sector savings defined as $$S=Y-T-C-I$$ ? afterall, savings is the money you have left over after you net off from your income ALL of what you have paid out.

$$Y, T , C$$ And $$I$$ are the standard things every 1st year macro class in the world teaches they are (output/income/outgo , taxes, consumption , and investment)

• What is $T$? And what is the definition of savings that is not satisfactory to you, and why? Please include this information in your question, not as an answer to this comment. Thank you. – Alecos Papadopoulos Jan 3 at 19:07
• T is taxes. all these letters are from 1st year macroeconomics , i am sure everyone knows them! – Randor Jan 4 at 6:49
• Why would one subtract investments? These are (presumably, as you don't provide a model) done by firms and equal private savings in a closed economy. Further assuming $T$ is an income tax, $S=Y-T-C$ seems alright. – E. Sommer Jan 5 at 17:18
• a) households do lots of investment eg when new houses are built b) ultimately firms are owned by households so a firms investment is a households investment – Randor Jan 6 at 15:43

In a closed economy, which is what you have because you are not considering net exports, I=S, so the definition of output is Y=C+I+G. This is because output equals total final-good expenditure on consumption, government final good expenditure (i.e. excluding transfers to consumers like benefits), and investment.

Note that S is not included in this definition because to do so would be to double-count investment (however I could substitute it in for I. Likewise, I have included G, or government expenditure, instead of T because this allows for a more flexible definition where the government doesn't necessarily run a balanced budget. However, not that if G=T then you could substitute T into the equation instead.

If you substitute S=I and then rearrange for S you will fine you get S=Y-C-G, which I presume is the definition you have come across previously.

• u have totally lost me. why are u saying S=I . please prove that! – Randor Jan 6 at 19:07
• also i believe the standard equation of S is S=Y-T-C and this applies in an open economy too – Randor Jan 6 at 19:09
• S=I because Y=C+I+G in national accounts and also Y=C+S+T, and under our balanced budget simplification G=T; these are 2 equivalent ways to add up income. Intuitively think of it as the fact you can measure income by adding private and public spending, and investment (the first one), and on the other hand you can add up public and private "income" to get total income (the second one). Note that private income, in the second case, is just C+S because all our income is spent or saved – Slom Jan 7 at 20:14
• we have gone off topic but anyway regarding your formulation S=I i think this is true only in a 1 sector economy. when u add gov sector then the standard equations give you S+T-G=I. And for the OP, Patricio's answer is starting to help. she says simply that S INCLUDES I by definition. (i still am not so clear why define it that way) – Randor Jan 8 at 6:50

Savings are defined as that part of income that is not spent on consumption nor paid in taxes to the government. We do not focus on what is done with savings but, rather, on how much of the disposable income is not spent on consumption. In colloquial terms investment has a wider meaning than in economics. For instance we'd say "I've invested \\$10.000 in the stock market." For economists, in order for an expenditure to qualify as investment, it needs to be on capital goods. Therefore, buying shares of stock is not considered as an investment, but just an allocation of savings.

• but what is the value in such a definition of savings? if you had bought a new house , then that would be Investment, and surely its silly not to deduct that Investment spending too when calculating savings – Randor Jan 7 at 19:23
• If you buy a new house, you're doing two things, saving (refraining from consuming) and investing (using the amount you didn't consume to buy capital goods). Note that it must be a new house, otherwise this wouldn't count as an investment either. – Patricio Jan 8 at 4:18
• so we are saying that Saving includes all Investment. And therefore that the true monetary savings, ie money (cash) saved over the year, equals S-I right? – Randor Jan 8 at 8:04
• fred.stlouisfed.org/release/… NIPA Table 5.1. Saving and Investment by Sector: is it correct that Line 1 (gross saving) = S and line 2 (net saving) = S-I ? – Randor Jan 8 at 8:49