Investment and Savings

00:01 Hello and welcome back to your online presentation of macroeconomics.

00:04 My name is James DeNicco and this presentation were we be talking about investment and savings.

00:10 So we're continuing to talk about the different components of GDP.

00:14 Last time it was consumption.

00:15 Now this time it's investment and both of them are related to savings.

00:20 So specifically, we're going to be looking where do people save money? We'll put some reality to this.

00:25 Where does this actually take place? We're going to look at the demand curves for investment and the supply curves for savings. We're going to look at what shifts those different lines and how that changes our equilibrium or where supply equals demand.

00:41 We'll look at the relationship between investment savings and net exports in an open economy.

00:47 In a closed economy, we're going to assume away those net exports.

00:50 But then we'll open up the economy to allow net exports.

00:53 We're allowing trade.

00:54 Then we're going to look at what net capital outflows are.

00:58 That's the asset side of trade.

01:00 So somebody gives you goods and services, you give them assets in return.

01:05 And we're also going to look at the relationship between net exports.

01:09 Net capital outflows in an open economy.

01:13 So first, where does all this take place? Well, savings takes place in these financial systems.

01:18 Those are just a group of institutions in the economy that help to match one person's savings with another person's investment.

01:26 So you save your money.

01:28 You give your money to somebody.

01:29 They owe you it back later on, but they're going to use those borrowings to invest. So financial markets, financial markets, they're institutions which people can provide savings directly to investors.

01:42 There's a couple types of those stocks and bonds.

01:45 We most of us have heard of stocks and bonds.

01:47 They're a little different.

01:49 The bond market, that's like an IOU.

01:51 So I give a corporation some money.

01:54 They gave me a little bond certificate or a corporate bond that says, I owe you that money back with some interest.

02:00 Then the corporation can take that money and they can invest with it.

02:04 Stocks, that's when you buy ownership in a company.

02:07 So I go, there's a publicly traded company, I buy a little piece of it.

02:11 They owe me that back at some point, right? I'm an owner and they use the money that I give to them and they use it to invest or try to expand their company.

02:21 So we're talking about investment here.

02:22 Remember, that's buying physical capital when the firm buys tools and equipment and factories and materials to produce final goods and services.

02:31 It's also inventory investment.

02:33 It's also the purchase of new structures when people buy new homes or they build additions onto their homes.

02:40 So these are the financial markets.

02:41 This is how you match people directly, savers and investors matching them directly. You also can do it indirectly through financial intermediaries.

02:51 So those are banks.

02:52 You go to the bank, you put your money in the bank, they pay you an interest on that money.

02:57 Then they turn around and they loan the bank out to investors.

03:00 So they loan it out and they charge a slightly higher interest rate than you're giving than they're giving you for your savings.

03:06 That's how banks make money.

03:07 Or one of the ways that banks make money.

03:10 You can also buy into a mutual fund.

03:12 So you buy into a mutual fund and then they have a portfolio of stocks and bonds that they try to make money on and your mutual fund can grow in value.

03:20 So those are the indirect ways that you can provide savings to investors directly or indirectly.

03:27 This is where it takes place in the real world, right? So now we've seen where it takes place.

03:32 Let's take a look at some of the mechanics.

03:35 So here we have our supply and demand graph.

03:38 All right. So our demand is going to be investment demand.

03:42 So that is demand for loanable funds.

03:46 The supply that's our savings supply, I call it.

03:49 That's our supply of loanable funds.

03:53 So we're going to see that investment demand is downward sloping.

03:57 In all our graphs, we have demand downward sloping here.

04:00 Supply is going to be upward sloping.

04:02 So let's take a look at why we look on the vertical axis here.

04:07 And it's the real interest rate.

04:09 So why is the real interest rate goes down? Does investment increase or the demand for loanable funds increase? Well, the real interest rate represents the opportunity cost of investment.

04:22 So whether you're borrowing money to invest or you're taking some of your savings and investing, it's going to represent the opportunity.

04:29 Cost is just whether it's direct or indirect.

04:32 If you're borrowing money to buy physical capital, then you pay a real interest on the money that you borrowed.

04:38 That's a direct opportunity cost.

04:40 If you have some money in your savings and you take it and you buy physical capital, well then you're missing out on the real interest that that money could earn in a savings account. That's an indirect opportunity cost.

04:52 Either way, it's the cost of investment.

04:54 As the real interest rate goes down, the cost of investment goes down.

04:58 You're more likely to invest.

05:00 You demand more loanable funds.

05:03 Supply is upward sloping because the real interest rate goes up.

05:07 We know from our two period consumer model that that incentivizes us to save more. We want to save more money as the real interest rate goes up because the return on our savings goes up.

05:18 So we have an upward, upward sloping supply curve and our downward sloping demand curve where they come together that represents our market equilibrium.

05:27 So we have a market equilibrium or market clearing, real interest rate, and we have our market equilibrium level of supply and demand or savings and investment. Let's define our savings here.

05:41 So in the two period consumer model, we were looking at individuals, we said it's our current income minus our current consumption.

05:48 Here we're going to have our national savings.

05:51 So our national savings is defined as GDP, which we know from our GDP series or a GDP presentation.

05:58 That is our production.

06:00 It's also our income, it's our national income.

06:03 So you take away consumption, which is the spending by the households and the government purchases, which is the spending by the government.

06:10 Whatever's left over is our savings here.

06:13 First, we're going to assume we're in a closed economy.

06:16 There's no net exports.

06:17 So we'll keep it simple at first.

06:19 Later on, we'll open it up so that there's net exports.

06:21 Without net exports, you're going to see that in an economy, savings equals investment.

06:27 So GDP is Y, equals C plus I plus G in a closed economy.

06:34 So if we define national savings as Y, minus C, minus G, the national savings equals investment.

06:42 Savings equals investment.

06:45 Now, let's play a little game here so we can look at both private savings and public savings. We're going to add and subtract taxes doesn't change the equation at all.

06:55 Right. I add one, I subtract one, they cancel out.

06:58 So we're adding them, subtract, subtracting taxes.

07:02 We can move things around so that we see savings equals private savings plus public savings.

07:08 The private savings that's our income, minus our consumption, minus the taxes that the government takes away.

07:15 So we make some money, the government takes some in taxes.

07:18 We have a disposable income left over.

07:20 We consume with some of that money, what's ever left over.

07:23 That's our private savings.

07:25 We also have our public savings.

07:27 So that's the money the government takes in, in taxes, minus what they expend in government expenditures.

07:33 So taxes minus government spending.

07:35 If taxes are greater than government spending, that's a government surplus.

07:40 If taxes are less than government spending, that's a government deficit.

07:45 Right? That's a fiscal deficit.

07:47 So taxes greater than government spending, fiscal surplus taxes less than government spending. Fiscal deficit.

07:53 All right. So we've defined our national savings here.

07:56 Now, let's go back to our graph and see how changes in some variables will shift the graph around. We'll shift some of our curves.

08:04 So first, how about an increase in current income? Well, now we've got some synergy, right? We're going back to our two period consumer model and we're learning we're using a little bit what we learned then and move it into our savings and investment model.

08:17 So an increase in current income, we know we want to increase our consumption in this period, but we also want to increase our consumption in the next period.

08:26 Right. We want to smooth out our consumption.

08:29 So in order to increase our consumption in the next period, we have to save a little bit of that money we're going to make now.

08:36 So an increase in savings, that's a shift to the right.

08:39 All right increases in the these graphs move along to the right.

08:43 So along the horizontal axis and increase in savings goes to the right.

08:47 So saving shifts that way.

08:49 So there's more money, there's more loanable funds.

08:53 So as there's more loanable funds, the price of those loanable funds goes down, the real interest rate comes down.

08:59 As the real interest rate comes down, you move along the investment demand curve.

09:04 There's a higher demand for those loanable funds because the opportunity cost goes down. So we have a lower market clearing equilibrium, real interest rate and a higher equilibrium level of supply and demand or savings investment with an increase in current income.

09:21 How about an increase in future income? Well, we're going to get some more money later down the line.

09:26 We know again, we want to smooth out that consumption, so we increase our consumption later, but we also increase it now.

09:33 In order to do that, we need to decrease our savings.

09:36 So that's a leftward shift in the savings supply curve.

09:40 As that happens, there's less loanable funds, there's less of a supply.

09:45 So that's going to raise the price of those loanable funds.

09:48 The real interest rates going to go up as that happens, the opportunity cost of investment increases and we move along the investment demand curve to the left.

09:58 So we'll have a higher equilibrium market clearing real interest rate and a lower equilibrium level of supply and demand or savings and investment.

10:10 How about now if the government spends more money without changing taxes? Well, if you look back to our national savings equation, the public savings, that's taxes minus government spending.

10:23 So if government spending goes up without a change in taxes, that's a decrease in national savings.

10:30 So when that happens, we say the crowding out effect can take place.

10:34 You see a leftward shift in the savings supply curve.

10:38 There's. Less loanable funds.

10:40 So the price of loanable funds goes up again.

10:43 That raises the market clearing real interest rate or the price of the loanable funds and crowds out private investment.

10:51 That's what the crowding out effect is public spending crowding out private investment because it decreases national savings and raises the price of those loanable funds or increases the opportunity cost of investment.

11:07 So now we've covered the saving side.

11:08 Let's talk a little bit about the demand side or the investment side.

11:13 We're going to go back to a micro example and build up from our micro to our macro.

11:18 So last time we talked about Coca-Cola Hoagies.

11:20 Right, or our spicy sweet ham, which is delicious.

11:24 Now we'll talk about pizza, another one of my favorites.

11:27 So Jimmy's Pizza Palace.

11:28 I own a pizza shop and I'm selling my pizzas for $10.

11:32 You even get a drink with that? That's a pretty good deal.

11:34 All right. So we have all the information we need to decide how much capital this individual firm demands.

11:41 And then we'll just say every firms alike, and we'll just aggregate it up for simplicity's sake to keep the model simple.

11:47 So here we are going to see that the price of pizzas, $10, the price of our capital is 1000, our real interest rate is 10% or 0.1, and our depreciation rate is 8% or 0.08.

12:01 The only difference here is from Labor really is going to be how we calculate our marginal cost or the additional cost of another unit of capital.

12:10 So we have our production schedule, our number of ovens and how many pizzas we can produce with those ovens.

12:16 The first thing we need to do is find our marginal product of capital or the additional production we get from another unit of capital.

12:23 In order to do that, we just subtract.

12:25 We say the first one brings in 26, so the marginal product is going to be 26.

12:29 The first oven brings in 26 pizzas.

12:32 Now our second oven, we're up to 50 pizzas.

12:35 But what does that bring in? 50 -26 is 24.

12:38 So it brought in 24 pizzas.

12:40 We do that all the way down the line.

12:42 The six oven that we get brings in, we have now have 126 pizzas in total. But how much extra did it bring in? 126 -110 is 16.

12:52 So the marginal product of capital of that six oven is 16 pizzas. So now we have the product side or the marginal product side.

13:01 Let's take a look at the cost side.

13:04 The cost are the marginal cost when you're looking at purchasing capital is what we call the user cost of capital.

13:11 Let's look a little closer at that.

13:13 The user cost of capital is the cost of using a piece of equipment per time.

13:18 So we think of this whole thing in per units of time.

13:20 How many pizzas can the oven make per unit of time? So as you use your capital, it's going to lose value, all right.

13:28 It's going to lose value because it depreciates.

13:31 Also, you're going to have to pay a cost on that.

13:33 You're going to have to pay the real interest rate.

13:36 There's two pieces to the user cost of capital, the real interest rate and the depreciation rate.

13:41 So we can calculate the user cost of capital here, which is the nominal marginal cost of purchasing a unit of capital.

13:49 Nominal means in dollar terms.

13:52 So how many dollars does it cost us to acquire another unit of capital? So it's going to be the price of the capital times, the real interest rate plus the depreciation rate.

14:02 So let's look at those two pieces a little closer.

14:04 The real interest rate, again, that's the opportunity cost of investment, whether you're borrowing and paying that real interest rate on those borrowings or whether you're using your savings and missing out on the real interest rate you could be earning if you left that money in the bank.

14:19 So say the interest rate that you could get is 10%.

14:22 You lose 10% a month.

14:24 All right. The other part of that is the depreciation rate, how the value of that oven erodes. Maybe the oven wears down as you use it.

14:31 It gets cracks in and it's not it's efficient.

14:33 So it's not as valuable or just used equipment as a stigma to it.

14:38 Right. You go to buy a used car and you're not going to pay a premium for that.

14:42 You buy a car new as soon as you drive it off the lot.

14:44 You just lost a lot of money, right? The car loses a lot of value because people aren't willing to pay a premium for a used vehicle.

14:52 So as time goes on, the user cost of capital is made up of the real interest rate and the depreciation rate.

15:01 So now let's go back to our chart and look at our user cost of capital or our marginal cost of adding an additional unit of capital.

15:08 So we see we're going to have our $1,000 times 0.18 or 1000 times our real interest rate plus our depreciation rate.

15:17 So 1000 times, 0.18 is $180.

15:21 Every unit of capital costs us $180 per unit of time.

15:25 The first one, 180, the second 180, all the way down the line.

15:29 The sixth one cost us an additional $180.

15:33 We can take those nominal terms and turn them into real terms.

15:36 So we go from dollar figures to quantity.

15:38 Here the quantity is in terms of pizza.

15:40 We divide by the price of the pizzas.

15:43 180 divided by ten is 18.

15:46 Each unit of capital costs us 18 pizzas.

15:49 So now we can decide how many units of capital we want to purchase.

15:53 We take a look at the marginal benefit of the first one.

15:55 It brings in 20 pizzas, 26 pizzas.

15:58 It costs us 18 pizzas.

15:59 We want it. The second one brings it in 24 pizzas, costs us 18 pizzas.

16:05 We want it. The marginal benefit is greater than the marginal cost.

16:09 Go on and down the line.

16:10 The third one, 22 is greater than 18.

16:12 We want it 20 is greater than 18.

16:14 We want it the fifth one, 18 is equal to 18.

16:17 We'll take it. All right.

16:19 It's our indifference point.

16:20 If it doesn't cost us more than that benefits us, we'll take it.

16:23 The sixth one brings in 16 pizzas, but it costs us 18 pizzas.

16:27 We don't want it right.

16:29 We don't want that one. It costs us more than it makes us.

16:32 We're going to strike that off the list.

16:33 We're going to stop at five.

16:34 We want five units of capital.

16:37 So that's the micro.

16:38 We can take a look at it in graphic form.

16:40 We can illustrate it.

16:42 A picture always helps.

16:43 I think it at least helps me.

16:44 So here we're going to see this downward sloping curve that's our marginal product of capital. If you go back and look, you're going to see that the marginal product capital is diminishing.

16:54 We have diminishing returns here.

16:56 Again, it's the idea once again of the farmer who is telling the land by hand. He gets himself a unit of capital, he gets himself a tractor.

17:05 He sees these massive increases in productivity.

17:08 He gets himself a second unit of capital, second tractor.

17:12 Now he's more productive because when the first one is in the shop, he doesn't have to stop. He can use the second one, but the increases in productivity aren't as large. Most of the time the second tractor is sitting there idle.

17:23 He's using the first one, but when the first one is down, he can use the second one.

17:28 He's more productive.

17:29 But the increase isn't like going from his hand to the first tractor.

17:33 That's a very large increase.

17:34 So again, we see these diminishing marginal returns.

17:38 The way we set it up, we have this constant marginal cost.

17:42 Any time the marginal benefit is greater than the marginal cost, that additional unit of capital is bringing in profit.

17:49 So this whole area in this triangle is profit that we can exploit.

17:53 So we want to exploit it all the way up to this point right here.

17:57 That's the capital we want to purchase.

17:59 So again, this is the micro side.

18:01 Now, let's take it from the micro to the macro.

18:04 Anything that's going to increase that marginal product of capital, you'll see it shifts that curve up.

18:09 And now we go from the small triangle of profit that we can take advantage of, to this large triangle of profit that we can take advantage of.

18:17 We increase the capital that we want to purchase.

18:20 We increase our demand as demand goes up.

18:23 There's a rightward shift in the investment demand curve, the demand for loanable funds that increases the price of the loanable funds.

18:30 So the market clearing real interest rate goes up and we have a larger level of equilibrium, supply and demand or savings and investment.

18:39 You could also have a change in the marginal cost.

18:41 So if the marginal cost goes up, you'll be demanding less.

18:46 So let's open it up.

18:48 Let's allow for trade, let's allow for net exports.

18:51 So now GDP again, like we had it before, is going to equal consumption plus investment plus government purchases plus net exports.

19:00 We'll still define national savings as GDP minus consumption, minus government expenditures.

19:07 So savings is whatever production is left over after you take away consumption and after you take away government expenditures.

19:15 So let's rearrange our equations a little bit here now with net exports.

19:19 And once you get down to the bottom here, you're going to see that net exports equals savings minus investment.

19:26 If investment is greater than savings, net exports is going to be less than zero.

19:30 That should make sense if we demand more production than is in our country.

19:35 We have to go outside the country to get it.

19:38 We have to import it.

19:39 Net exports as exports minus imports.

19:42 If imports are greater than exports, net exports are less than zero.

19:46 So again, savings is whatever production is left over after consumption and government expenditures.

19:53 If our investment demand is greater than that, we have to go outside the country to get it. Just the opposite is true of savings is greater than investment.

20:01 So if our investment demand is less than the production that's left over within the country, we're going to export it to other countries and net exports will be greater than zero. So we can take that to the graph.

20:14 So let's look at that.

20:15 Here are a is what we're going to call our all turkey interest rate.

20:19 That's the interest rate that would prevail in a closed economy, but it's no longer necessary. We're going to see here if the real world interest rate is above our autarky interest rate. The opportunity cost of investment has gone up because now we can get a higher return on our savings somewhere else.

20:36 So we're going to want to increase our savings above our investment.

20:41 So you'll see as you go up, net exports is going to get greater and greater and greater net exports is greater than zero when savings is greater than investment.

20:51 On the bottom here, if the real world interest rate is lower than our autarky interest rate, then the opportunity cost of investment is gone down.

20:59 We can borrow funds cheaper.

21:01 So you're going to want to increase your investment demand above your savings.

21:05 As that happens, net exports becomes more negative.

21:09 So in an open economy, we have access to these other interest rates, these real world interest rates.

21:16 So it's going to change our opportunity.

21:18 Cost of investment.

21:19 No longer are we subject to investment equaling savings.

21:23 If we want investment greater than savings or greater savings greater investment, we can access that now through the rest of the world.

21:32 Let's talk about the net capital outflows now.

21:34 That's the asset side of it.

21:36 So it's kind of a complicated definition.

21:39 It's the change in domestic ownership of foreign assets, minus the change in foreign ownership of domestic assets.

21:46 It sounds complicated, but all net capital outflows are it's just a change of assets for goods and services.

21:53 So net exports have to equal net capital outflows.

21:56 It's an identity.

21:58 It's from accounting, right? The left hand side of the ledger has to equal the right hand side of the ledger.

22:02 Debits have to equal credits here for every good and service exchanged.

22:07 There has to be an asset, an asset exchange.

22:10 So let's do it. Look at an example here.

22:12 $100 in cheesesteaks are exported to Italy from the United States.

22:17 I come from Philadelphia area, so cheesesteaks are specialty.

22:20 So I like to talk about them.

22:22 So $100 in cheesesteaks are exported to Italy.

22:26 So that's an increase in our exports of $100.

22:30 Italy has to give us $100 in return.

22:33 That's going to increase our net capital outflows because Italy is relinquishing their foreign ownership of our domestic assets.

22:42 So the two sides of that equation, the net change in domestic ownership of foreign assets, minus the net change of foreign ownership of domestic assets, the foreign ownership of domestic assets are going down.

22:55 The negative side is going down.

22:57 So net capital outflows are more positive.

23:00 So again, it's just an identity.

23:03 Every exchange of goods and services has to have assets in return.

23:08 Maybe we can make some more sense of it here on this slide.

23:10 So say savings is greater than investment in the United States.

23:15 What that saying is with that extra savings, we have John Smith here.

23:19 He's going to buy stocks of Volkswagen, uses those extra savings to buy a piece of Volkswagen.

23:25 Then Volkswagen is going to go ahead.

23:27 They're going to use those extra savings.

23:29 They're going to borrow that money and they're going to invest with it.

23:33 On the flip side, say Friedrich Hayek, who is a famous economist that I kind of enjoy reading Friedrich Hayek buy stocks of GM in the US with his savings. That means GM is using those borrowings, using Friedrich Hayek's savings to do its own investment.

23:52 So you see again, all we're saying with net capital outflows is that net capital outflows have to equal net exports for every trade in goods and services. There has to be assets coming in return.

24:05 That's all that is.

24:08 So what might change these net capital outflows a little bit? We'll talk about four factors.

24:13 One, an increase in the real interest rate on foreign assets.

24:18 If that happens domestically, we're going to want more foreign assets.

24:23 If there's a bigger return on those foreign assets, we're going to want to increase our domestic ownership of those foreign assets for sure.

24:30 That would drive up net capital outflows if there's an increase in the real interest rate on domestic assets here in number two, net capital outflows are going to be negative. We're going to want less foreign assets and more of our own assets.

24:44 Also, foreigners are going to want to acquire more of our domestic assets. That's going to drive down net capital outflows.

24:52 The last two are a little more obvious, I would say.

24:55 So perceived economic political risk of holding assets abroad.

24:59 So if a country all of a sudden becomes war torn, you're not going to want to buy their assets. You're going to want to relinquish relinquish your domestic ownership of those foreign assets because it becomes riskier.

25:10 The fourth one, government policies that affect foreign ownership of domestic assets.

25:15 If there's taxes on the ownership of foreign assets, you're probably going to want less of those foreign assets.

25:20 So again, net capital outflows will go down.

25:23 So those are four factors that will affect those net capital outflows.

25:28 Let's look at a graph. I always like looking at pictures.

25:30 Pictures make it fun.

25:32 All right. So we're going to assume here that we're in a two country world to make things simple. You could have all the countries if you want to, but it wouldn't fit on the slide. So we're going to do something that fits on the slide here.

25:42 We're going to say the two countries in this world are the United States and Germany.

25:47 All right. So at the world level, we still need it to be that savings equals investment. Net net exports have to equal zero and net net capital outflows have to equal zero.

25:59 It's just the idea for everything being imported.

26:01 Something has to be exported for every dollar being given.

26:05 Somebody has to receive that dollar.

26:07 So everything still needs the net out at the world level, but at the country level it doesn't. So in the United States here, we're going to see the real world interest rate is lower than our all Turkey interest rate.

26:18 Again, that means the opportunity cost of investment is gone down.

26:22 So we want to increase our investment over our savings.

26:26 That means we'll have negative net exports and negative net capital outflow.

26:31 That means for Germany it has to be exactly equal and opposite.

26:35 So the real interest rate they see at home is lower than the real world interest rate.

26:40 So the opportunity cost of investment for them is going up.

26:43 They want to save more than they invest.

26:46 Their net exports are greater than zero.

26:48 Their net capital outflows are greater than zero, and it has to be equal and opposite to the United States.

26:54 So the world level, net net exports and net net capital outflows, zero out and savings equals investment.

27:02 So again, open economy, it doesn't have to be true at the country level that savings equals investment, but at the world level it still has to be true.

27:12 So what have we learned here in this presentation? We learn where people can save their money and how those savings are used.

27:19 We learn that savings equals investment in a closed economy, but not necessarily so in an open economy.

27:25 We learn that changes in income will shift our savings supply curve and changes in the marginal product of capital and the user cost of capital will shave our, will shift our investment demand curve and we know what net capital outflows are and we know the relationship to net exports.

27:42 So that's what we've covered in this presentation.

27:44 Thank you.