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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!(3 votes)- 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.(9 votes)

- 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?(4 votes)- 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.(2 votes)

- 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)

## Video transcript

- [Instructor] In this
video we are going to use the GDP equation that we have seen before to think about how national
savings relates to investment. And really it's a way to
algebraically manipulate things to ensure that it fits with our intuition. So another way to think about a GDP is it's the same thing as national income, which we donate with a capital letter Y. And GDP or national income, we can account for it by saying, hey, that's going to be
the sum of consumption plus investment plus government
spending in a closed economy. We could also think about an open economy where you have net
exports right over here, but let's just focus on
a closed economy for now. So I'm gonna just actually label this. We're gonna deal with a
closed, closed economy. In a future video I will
open the economy up. But how could we solve for savings? Well, what happens if
we subtract consumption and government spending from
both sides of this equation? Well then you're gonna
have national income minus consumption, minus
government spending, is equal to investment. Now, what is another way of thinking about this left-hand side of this equation? So at a national level this is the income minus how much is being consumed and how much the government is spending. So it's income minus the
different types of spending. Well, you could view
this as national savings. National savings. And we see here this identity
that national savings, which is often denoted with a capital S, is equal to investment. And if that isn't
intuitive for you at first, just think about it at
a kind of human scale. If I am saving things and I
am putting it into a bank, that bank will then lend that money that can be used for investment. And we can break this down even more if we wanna think about taxes. So let's just say T is equal to taxes. So let's just think about
the private economy first. So if we think about the national income minus consumption spending, and then folks have
got to pay their taxes. So minus taxes. And then where do those taxes go? Well, they go to the government, so they stay in the economy. So notice, I'm not changing this equation, I'm just subtracting taxes
and then adding taxes. And then I subtract from
that government spending. These two equations are equivalent and this is going to be equal to our investment in our closed economy. Now, if you look at this
left-hand side right over here, you could view this as private savings. This is the national income, minus how much is being consumed, minus how much is being
paid to the government. So this is private, private savings. And if you look at the second part, the taxes the government gets minus how much the government spends, this you could view as public savings. Public savings. In most countries this
is neutral to negative, so it's actually the
public savings are negative 'cause the government spends more than the amount of revenue gets in taxes. But either way you could see the T minus G would be the public savings, and you add public savings
and private savings together, you get national savings.