Savings Equal Investment - Video Tutorials & Practice Problems

Saving Equals Investment

Alright, So, a key identity in this class is that the amount of savings that there are from the household is going to equal the amount of investments by the firm's let's check that out. So savings. Remember savings is when there's current consumption is less than current output. Right? So this means that the households are not consuming as much as there as there is an 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 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 household output households in quotations, because firms can buy household investments as well. But in that idea, they're kind of treated like households in the way we think about financial investments. So, this is things like stocks and bonds 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 this is things like factories, machinery, right? Things like that are what we're talking about when we talk about investments, things that increase future output. Like in our definition up here increasing future output. All right. So, now, what we're gonna do is we're gonna 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, remember when we were talking about GDP um we used what was called the expenditure approach to calculate GDP. Do you guys remember when we did that? We're gonna review it in just a second. So expenditures is thinking, okay, all the money that's 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, well that 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 gonna call GDP. Why here? Okay, why why is going to be our variable for G. D. P. 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. What was the next one? It was C. Plus consumption plus investment plus government purchases plus net exports. I'm sure you guys remember that we went through it quite a bit right? C. Plus I plus G plus N. X. Right? C. Plus I plus G. Plus N. X. That is our GDP equation. And now we're gonna go through a little bit of of algebra to reformat that equation. The first thing we're gonna do to keep things simple is we're gonna 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 their trading with other countries so they're gonna be exporting stuff importing stuff leading to net exports. However we're gonna deal with a closed economy to make things a little simple. So closed economy does not trade with other countries. So the net exports, what do you think in a closed economy if their exports are zero, they're not selling anything to other countries, their imports are zero. They're not buying things from any other country. Well their net exports are going to be zero, right? There's gonna be no net exports. So in a closed economy, let's restate our our GDP equation here. So G. D. P. R. Income there is going to equal the consumption plus the investment plus the government purchases. And there's no net exports. Right? We're gonna 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 Vario 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 firm's investing here and then we've got government purchases by the government. Right. The government working over here. So the government making purchases. So the next thing we wanna 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 let's do that over here, Y. Equals C. Plus I plus G. Well if we subtract C. And subtract G from both sides, what are we left with? Why minus C minus G. Equals I write why being our GDP our total income minus the consumption minus the government purchases equals investment. So why minus C minus 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 consume that and the government purchases well, the government didn't save that either. Right? They purchase stuff, they were in essence doing their consumption government consumption in that case. Well, everything that's left over is our savings, right? So let's that's exactly what we have here. If we take all the all the income, the total income of why minus the consumption, what we consumed minus what the government purchased, we're left with our national savings. And what did why minus C minus G. Equaled why minus c minus 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 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 Safe 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 re watch how we solved 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. Why 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 is households, I'll put H. H. 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 gonna 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 gonna 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 are 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 gonna have why 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 gonna 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 gonna 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 plus T. So the negative T. And the positive T cancel out, and we're just left with y minus c minus G. Right? We still have y minus c minus G. All we did was take away the taxes from the households added 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 why minus c minus 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 minus c minus T. And the public savings are t minus 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. 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 it's spending, right? So we'll have a surplus. They have excess savings in that case. However, what what's been happening recently in the U. S. 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 gonna talk about how this 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, uh, affects this. Alright, let's do that in the next video.

Savings Equals Investment in an Open Economy

Alright, 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 deals with the savings investment identity that we've 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 why minus C minus G minus net minus 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 gonna 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 equals C plus I plus G plus N. X. Right? Well, if we solved for i in that case the investment, what we would be left with y minus c minus G minus N X equals 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 um basically imports coming in uh that are greater than our exports. So we've got this inflow of things coming into our country, well, that is going to be increasing our investment in the short term. So what we have is net 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, um 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 gonna have our national savings that we discussed above plus this net capital inflow, that's what's gonna equal our investment in this case. So where we had investment, equal 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 uh 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. All right. So in that case the investment would be lower with a negative N. C. I would have a net capital outflow in that case. Alright. 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.