Savings Equal Investment - Online Tutor, Practice Problems & Exam Prep

The identity of savings equaling investment is crucial in economics. In a closed economy, national savings (Y - C - G) equals investment (I), where Y is GDP, C is consumption, and G is government purchases. Private savings are calculated as (Y - C - T), while public savings are (T - G). In an open economy, net exports (NX) affect this relationship, with investment being financed by net capital inflow when imports exceed exports. Understanding these concepts is essential for grasping economic dynamics and the impact of fiscal policies.

Saving Equals Investment

Alright. So, a key identity in this class is that the amount of savings from the households is going to equal the amount of investments by the firms. Let's check that out. So, savings, remember, savings is when current consumption is less than current output, right? This means that the households are not consuming as much as there is in output. So, a bit is being saved, and this is done by the households, right? The households do the savings, and investment. Well, the current resources are devoted to increasing future output. That's how we define investment in previous videos, and this is done by the firms, right? The firms are investing in future output, right? And remember, as we've discussed, the term investment, it's different in economics than what you're used to when we talk about investments. Financial investments are made by households, right? Generally households, I'll put "households" in quotations because firms can buy investments as well, but in that idea, they're kind of treated like households in the way we think about financial investments. So, this includes things like stocks and bonds, which are generally what we think of when we have financial investments. Okay? But however, in economics and in this identity when we're talking about savings equaling investment, we're talking about economic investments that are made by firms, Okay? And these include things like factories, machinery, right? Things like that are what we're talking about when we talk about investments. Things that increase future output, increasing future output. Alright? So now, what we're going to do is we're going to go through a little bit of algebra using our GDP equation to kind of solve for how savings equals investments. Are you guys excited? I know I am. Alright. Let's go ahead and do that now.

So, recall that when we did GDP, we used what was called the expenditure approach to calculate GDP. Do you guys remember? We're going to review it in just a second. So, expenditures are thinking okay, all the money that was spent well that has to equal the amount of production there was, right? The gross domestic product, what was produced, the value of the goods that were produced, right? Well, if we think about the expenditure, all the money that was spent on production must have been earned by someone, right? So, the total income equals the total expenditure. Expenditure is one end of the coin, income is the other end, right? If we think about all the money that was spent well it had to be earned by someone else. So when we think about GDP, we can think of it as the expenditure or we can think about it as the income. All the money earned by the nation, okay? So, we're going to call GDP Y here. Okay? Y is going to be our variable for GDP and that's going to be income in this case. All the money that's earned. So let's go ahead and refresh. Do you guys remember how we calculated GDP? There were four things that we added together to total GDP. I'll give you a hint. The first one was consumption (C) and what was the next one? It was C plus Investment (I) plus Government Purchases (G) plus Net Exports (NX). I'm sure you guys remember that. We went through it quite a bit, right? C+I+G+NX, that is our GDP equation and now we're going to go through a little bit of algebra to reformat that equation.

The first thing we're going to do to keep things simple is we're going to treat this as a closed economy. So, an open economy, first off, is an economy that trades with others. So, in an open economy, there is going to be net exports, right? An open economy would have net exports because they're trading with other countries. So, they're going to be exporting stuff, importing stuff, leading to net exports. However, we're going to deal with a closed economy to make things a little simple. So, a closed economy does not trade with other countries. So, the net exports, what do you think? In a closed economy, if their exports are 0, they're not selling anything to other countries, their imports are 0, they're not buying things from any other country. Well, their net exports are going to be 0, right? There's going to be no net exports. So, in a closed economy, let's restate our GDP equation here. So, GDP, our income there is going to equal the consumption plus the investment plus the government purchases and there's no net exports, right? We're going to take that variable out because we're in a closed economy. So what does that tell us? That in a closed economy, all the output it's either consumed, right? In the first variable consumed, invested, or purchased by the government, right? Consumption, investment, and government purchases. So, what does that tell us here? We've got the households consuming here. We've got the firms investing here, and then we've got government purchases by the government, right? The government is working over here. So, the government making purchases. So, the next thing we want to do is we want to solve for investment. Let's go ahead and solve for investment in this situation. So, we've got Y equals C plus I plus G.

So, Y equals C plus I plus G. Well, if we subtract C and subtract G from both sides, what are we left with? Y - C - G equals I, right? Y being our GDP, our total income minus the consumption, minus the government purchases equals investment. So Y - C - G equals investment, okay? Have I lost you so far? Nothing too crazy has happened. All we did was we closed off the economy to get rid of our net exports, and then we solved for investment by moving the consumption and government purchases to the other side.

So, this gives us a term called our national savings. If we think of all the income that gets made, right? All the income that's earned by the economy, by the nation, well, if we take away everything we consumed, well we didn't save that right? We consumed that and the government purchases well the government didn't save that either, right? They purchased stuff they were in essence doing their consumption, government consumption in that case. Well, everything that's left over is our savings, right? So, that's exactly what we have here. If we take all the income, the total income of Y minus the consumption what we consumed minus what the government purchased, we're left with our national savings. And what did Y - C - G equal? Y - C - G equals our investment, right? So, we can say that our national savings equals our investment, okay? So, remember that was the idea here is that savings equals investment. That's a key identity that we have in this course. Savings equals investment. So, when we talk about savings, we're talking about national savings in this case. That's the savings of the households, as well as the savings of the government. Okay? So, let's pause here. If you guys need a little refresher, maybe rewatch how we solve for savings equals investments. And then let's continue and we'll talk about this in a little more detail on the next page.

National Savings, Private Savings, and Public Savings

Alright, so let's break up National Savings just a little bit more. Right? Remember, National Savings, so let's start this box. Remember National Savings from the previous page: we started with the total income that's earned, y minus the consumption, c minus the government purchases G, right? That was our national savings. All the income that's earned, well, we take away what we consumed, we take away what the government purchased and everything else is the savings. The national savings. So let's break that down into the private savings which are households. I'll put HH for households and the public savings, which is the savings of the government, okay?

So let's start here with private savings. Private savings is the amount of income that the households have left after paying for consumption, but they also pay one more thing. They pay their taxes, right? Households have to pay for taxes. So we're going to take the effect of taxes into account here. So the private savings, it is the amount households have left after they pay for consumption and taxes. That's the household private savings and then the government public savings. Well guess what? The government, all the taxes that the households pay, the government receives it. So the amount of tax revenue, so this is like the income of the government is the tax revenue that the government has left after paying for its spending, those government purchases, right?

So what we're going to do is we're going to expand our equation a little bit. We before had income minus consumption minus government purchases, well let's split this up into our private savings and our public savings. Because the national savings is the sum of private and public savings, right? So let's go ahead and let's define what our private and public savings are, okay? So remember, private savings, the amount of income that households have left after paying for consumption and taxes. So, we're going to have Y, the income minus consumption minus taxes, right? Because now the private savings is the income minus the consumption and the taxes, right? That's what's going to be in our private savings. Now, what about the public savings? Those taxes that the households paid, well the government received it. So there's going to be a positive T there. There's this positive T which is the tax revenue of the government minus the government purchases of G. Okay? So notice right here we have a minus T and a plus T. So the negative T and the positive T cancel out and we're just left with Y - C - G. We still have Y - C - G. All we did was take away the taxes from the households, add it to the government, okay? So we just expanded the equation just a little bit right there and we're left actually I'll leave those boxes just to keep it a little clear. Y - C - G. is still there and all we did was move that tax money around. So what were we left with? We saw that the private savings are this Y - C - T and the public savings are T - G. Cool? So the national savings, it's the private savings plus the public savings. Okay? So all we did was expand that equation. Now when we talk about our public savings, this is the government, right? So the government is going to be raising some tax revenue and then spending some of the money. Well, what do you think happens? What do you think a budget surplus means? That means that the government's raising tax revenue but not spending all of it, right? They have a surplus. So when the government's tax revenue is greater than its spending. Let me make a little more space there. Is greater than its spending, right? So we'll have a surplus. They have excess savings in that case. However, what's been happening recently in the US is that they actually run a budget deficit. So, there's actually negative savings from the government because their tax revenue, the T does not cover the government purchases. The government purchases are more. so when the government tax revenue is less than the spending, they're spending more than they bring in, they run a deficit. They've got a budget deficit in that case. Cool? So this is just an expansion of that savings formula where we have our national savings equal to our private and our public savings, okay? All we did was add the effect of taxes into this equation. Cool? Let's pause here and in the next video, we're going to talk about how this relationship of savings and investment, how it occurs in an open economy. Remember, we've been talking about a closed economy so far, where we didn't have net exports, okay? So let's see how adding into that equation of exporting and importing, affects this, alright? Let's do that in the next video.

Savings Equals Investment in an Open Economy

All right, so in this introductory class they don't go into so much detail about this, but it's nice to know at least on a high level, how the net exports deal with the savings-investment identity that we've discussed so far. Okay. So savings equals investment, right? And we saw how that works in a closed economy. Now let's see how the addition of net exports will affect this. So when we think about exports and imports, if we're importing a lot of stuff and not exporting it, well, we're basically borrowing money, right? Because we're importing things but not covering it with our exports. So that money borrowed has to be repaid with interest, right? And if we're talking about borrowing it from other countries through this deficit relationship where we're running a trade deficit, we're basically importing more than we're exporting. What we're basically borrowing from these nations. So we have what's called a net capital inflow because our investment spending is being financed by funds borrowed from foreigners. Okay, because remember our relationship of Y−C−G−net exports in this case is going to equal investment but let's go ahead and see how this flows. So now, what we're going to have is investment spending being financed by foreign money. However, it comes at a national cost, right? Because now our nation as a whole has to pay this interest to a foreigner to finance this extra spending, right? So when we think about that extra variable of net exports, right? We had y=c+i+g+nx, right? Well, if we solved for I in that case, the investment, well we would be left with y−c−g−nx=I, Right? Because we have this extra variable now of net exports. So how does this work into the equation? Is that now we have what's called this net capital inflow. If we've got basically imports coming in that are greater than our exports, so we got this inflow of things coming into our country. Well that is going to be increasing our capital inflow where our imports are greater than our exports, so imports minus exports. So if we have the situation where we're importing more than we're exporting. Well that's going to finance our investment as well, right? Because of this net exports term. Basically being the opposite of that being exports minus imports. However, the idea here without getting into too much detail all you really need to know is that in an open economy, we're going to have our national savings that we've discussed above plus this net capital inflow that's what's going to equal our investment in this case. So where we had investment equals savings in an open economy well it's plus the net capital inflow and that's because if we are importing more than we're exporting, well that's going to help finance our investment as well, okay? So that's the whole idea when we open up the economy, if this idea of imports and exports are going to finance. Now what if we were exporting more than we're importing? Well that would decrease our investment right? Because we're exporting some of our savings to other countries basically in that case. Alright, so in that case the investment would be lower with a negative NCI. We'd have a net capital outflow in that case. All right? So don't worry too much about this. The main stuff that we want to remember from this video is how we had that savings to investment identity and how we calculated our public and private savings. Cool? With that said, let's go ahead and move on to the next video.

Here’s what students ask on this topic:

What is the relationship between savings and investment in a closed economy?

In a closed economy, the relationship between savings and investment is defined by the identity that national savings equals investment. This can be expressed using the GDP equation: $Y=C+I+G$, where $Y$ is GDP, $C$ is consumption, $I$ is investment, and $G$ is government purchases. By rearranging the equation to solve for investment, we get: $I=Y-C-G$. This shows that national savings, defined as $Y-C-G$, equals investment.

How do private and public savings contribute to national savings?

National savings is the sum of private and public savings. Private savings are the amount of income households have left after paying for consumption and taxes, expressed as $Y-C-T$, where $T$ represents taxes. Public savings are the tax revenue the government has left after its spending, expressed as $T-G$. Therefore, national savings can be written as the sum of private and public savings: $Y-C-G$.

What happens to the savings-investment identity in an open economy?

In an open economy, the savings-investment identity is affected by net exports (NX). The GDP equation becomes $Y=C+I+G+\mathrm{NX}$. Solving for investment, we get $I=Y-C-G-\mathrm{NX}$. In this context, investment is financed by national savings plus net capital inflow, which occurs when imports exceed exports. Thus, the equation becomes $I=S+\mathrm{NCI}$, where $\mathrm{NCI}$ is net capital inflow.

How does a budget deficit affect public savings?

A budget deficit occurs when the government's tax revenue is less than its spending. In terms of public savings, this means that $T<G$, where $T$ is tax revenue and $G$ is government spending. As a result, public savings become negative, contributing to a decrease in national savings. This can be expressed as $T-G<0$, indicating a deficit that reduces the overall savings available for investment.

What is the difference between financial investments and economic investments?

In economics, the term 'investment' refers to economic investments, which are expenditures on capital goods like factories, machinery, and equipment that increase future output. This is different from financial investments, which involve purchasing financial assets like stocks and bonds. Economic investments are made by firms to boost production capacity, while financial investments are typically made by households to earn returns. Understanding this distinction is crucial for grasping how savings translate into productive investments in the economy.