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### Course: AP®︎/College Macroeconomics>Unit 4

Lesson 7: The Market for loanable funds

# National savings and investment

The market for loanable funds brings savers and borrowers together. We can also represent the same idea using a mathematical model. In this video, learn about the savings and investment identity.

## Want to join the conversation?

• Why did he subtract taxes then add them back?
Help!
• It's really just a math trick to get taxes included into the equation. If you add and subtract something, you are basically adding zero. But when we do this with taxes it lets us rearrange the equation to be something more intuitive:

Y = C+G+I+X-M
is just the equation that represents GDP. But how is G paid for? Taxes! And where do those taxes come from? People who earn income and buy consumption goods. So we need to represent that taxes get taken away from income and are used to pay for government spending. We can use the math trick to do that:

so first assume a closed economy so X-M goes away:
Y = C+G + I
Y = C + G + I + T - T
Then rearrange:

Y - C = G + I + T - T
now Y-C is on its own. That's what is left out of income after you spend money on consumptions. If you didn't have to pay taxes, that would be your savings! But we do ( :'( ) so lets get taxes on the left hand side too:

(Y - C - T) = G + I - T
Y-C-T is something called private savings, which is what households have left over after consumption and taxes. But let's keep going until I is all by itself on the right hand side:

(Y - C - T) + T = G + I
(Y - C - T) + T - G = I
Now we also have T-G. Remember that Taxes pay for Government spending? So T-G is the budget surplus (or deficiit if it is negative. (T - G) is called public savings:
(Y - C - T) + (T - G) = I
Private Savings + Public Savings = I
Total Savings = I
S = I --> The savings must equal investment identity.
• I've never understood the savings argument.

If you spend money, it moves between depository accounts. This is the same as not spending money, thus savings does not increase investment (i.e. reducing C does not increase I).

The math used suggests that if C decreases, I increases. Besides that this doesn't seem to work from a reasoning perspective on banking, a decrease in C changes business sentiment and causes a reduction in I, as businesses begin storing financial capital instead of spending to expand (investment).

The model given seems to work in a world where spending is cash to cash and businesses keep their cash in a safe; it breaks in the way I describe where businesses bag up their excess cash and deposit it into banks at the end of the day or week (it's often the end of the day), and where many transactions are electronic.

Credit card transactions are particularly interesting: a person runs up a credit card for the month, then has no interest charge for the first month. The balance is notated, and interest will be charged if it's not paid the next month. The person then uses one of their three-per-month savings account withdrawals (no reserve requirement!) to pay down the credit card. The net effect of this scheme of electronic payment is the same as writing infinite checks from savings, thus savings accounts sort of behave as a checkable deposits account but with a lag on accounting.

In such an electronic transaction world, we have less and less cash outside of banks at any given time, and so what I describe about C and I here seems to become more true and the classical theory presented less true.

Am I missing something?
• Investment is not equal to loanable funds. The next lesson says:
Remember that in economics the word “investment” refers to spending by businesses on physical capital, inventories, and other business expenditures.

Specifically, if spending on consumption decreases, then unsold goods increase, which is investment.
• How to get the intuition that national savings equal investment? Intuitively, it looks to me that if we save the money, we are not using them. So we could not use them for investments. Please help. Thanks.
(1 vote)
• Why do we call Y as the National Income when this is really GDP in terms of expenditure?
(1 vote)
• GDP can be calculated as sum total of the factor income earned by households from firms in the economy. This is basically the total income people in the country receive as wages i.e, the national income.
(1 vote)
• I want to know what do people do in National Saving
(1 vote)
• Would savings be greater than investment if the government is running a budget deficit?
(1 vote)
• Why did he subtract taxes then add them back?
(1 vote)
• if people dont save money in banks then the saving will not not be equal to investment?
(1 vote)
• Clarification: National savings and investment are equivalent?
(1 vote)