Consumption and Savings

00:01 Welcome back to your online presentation of macroeconomics.

00:04 My name is James DeNicco.

00:06 This presentation will be about consumption and savings.

00:10 So over the next few presentations, we're going to be talking more specifically about the different components of GDP.

00:17 Here we'll be talking about consumption, of course.

00:20 So what exactly are we going to be doing? We're going to be looking at what savings is.

00:25 So there's this relationship between savings and consumption.

00:29 The more you consume now, the less you can save now, the more you save now, the less you can consume now.

00:35 So we'll be looking closely at that relationship.

00:38 We're going to be using what's called the two period consumer model to do that.

00:42 We'll also be looking at the relationship to income and savings and consumption.

00:47 As your income changes, how does that change the relationship between consumption and savings? And we'll also be taking a look at interest rates and how changes in interest rates incentivize you the more savings or more consumption now.

01:02 So first, let's take a look at some definitions.

01:05 So we'll define savings.

01:07 So here, savings is specifically going to be your current income minus your current consumption.

01:14 So if we're talking annually, it will be this year's income, minus this year's consumption.

01:20 Savings is what we call a flow variable.

01:22 It's measured per unit of time.

01:24 Whatever you define that unit of time to be, if it's weekly, it's my income this week, minus my consumption this week.

01:32 That's specifically what savings is here.

01:35 That's what we're going to define it as.

01:37 Wealth. That's different than your savings.

01:39 Wealth is a stock variable, so your savings now will turn into part of your wealth later on.

01:46 Your wealth specifically, again, are your assets minus your liabilities, your total assets minus your total liabilities, your savings rate.

01:56 That's going to be your savings divided by your income.

01:59 So the percentage of your income that you're saving, capital gains and capital losses, those are changes in the value of your assets.

02:08 So a capital gain, that's when there's an increase in the value of your assets.

02:12 Your stocks go up or you earn interest on your savings.

02:15 You call it your savings account.

02:17 But really, maybe it should be called your wealth account because again, savings are specifically your current income minus your current consumption.

02:25 Next period after that flow variable is measured in this period, next period, that'll be part of your wealth.

02:31 So capital gains are increases in the value of an asset.

02:34 Capital losses are decreases in the value of an asset.

02:38 So if you have a retirement plan and there's some sort of crisis that goes on, a financial crisis like in the United States in 2008, and a lot of people lose value on the retirement plans that would be a capital loss.

02:51 So one more time, your savings is a flow current income minus current consumption. Your wealth is a stock variable, your total assets minus your total liabilities. Your savings rate is the percent of your income that you save.

03:06 Capital gains are increases and the value of your assets and capital losses are decreases in the value of your assets.

03:13 So now that you understand the definitions, let's go forward and look at the life cycle of savings.

03:20 So you see here in this graph, what we have on the vertical axis is your income and your consumption.

03:27 Along the horizontal axis is your life line or your age.

03:31 So we're going to take a look at this line right here, this horizontal line that's constant across the graph, that's consumption.

03:39 What that's showing is consumption is balanced over time here.

03:43 It's constant over time.

03:44 That's not necessarily the way it's going to be.

03:47 We have a theory called the consumption smoothing theory that I'll get to in some later slides. That's what you want smooth and balanced levels of consumption over time. It doesn't have to be constant, however, but for purposes of this graph, we draw a constant.

04:01 Now the line that goes up and down, that's going to be your income.

04:05 So what you're going to see is early on in your life, you're going to be spending more than you bring in. That's a period of dissavings.

04:13 So probably a lot of you out there might have some student loans or you're taking loans out on your cars or some of you have mortgages you need to pay on.

04:22 So you're spending more than you're bringing in right now.

04:26 But as you move along, you get to your prime earning years.

04:29 This actually makes me feel a little bad because I guess I should be in my prime earning years. I hope that's not the case yet.

04:34 But as you move along here, you see you start to earn more than you spend.

04:39 So you're saving.

04:41 So what you're saving for is when you get to later in your life, say, around 65, you retire.

04:46 You want that nest egg, you want the money to live out the rest of your life.

04:51 So once you hit about 65, again, you're dissaving you're spending the money that you saved during your prime earning years.

04:59 So that's what the.

05:00 Savings lifecycle looks like for most of us.

05:03 It may be shifting to the right these days a little bit.

05:06 I don't know. We'll see.

05:09 All right. So why do you save whatever motivations for saving? Well, one or long term goals, things like you want to buy a house, you want to buy a car, you want to go on a nice vacation.

05:19 A lot of us don't have the money just sitting around to do those things.

05:22 So we have to set a plan.

05:24 We have to save to reach those goals.

05:27 Or it could be precautionary savings.

05:29 You never know when something's going to come up.

05:31 You get sick or you get hurt.

05:32 You have to spend money on hospital bills or you can't go to work.

05:35 They usually say you should have about six months worth of income sitting in your savings account for precautionary reasons.

05:43 Also bequest or inheritance.

05:45 Most of us hope we have parents that love us out there and a lot of our parents, they want to earn money so that they can leave something behind for their children.

05:53 Inheritance. Or if you're a philanthropist, you have a lot of money.

05:57 You want to leave your legacy behind.

05:59 You want to leave money to different causes or different universities.

06:02 That's another reason to save these bequest savings.

06:06 So those are our three main reasons to save your money.

06:10 So now let's talk about our model, our two period consumer model as the name portends.

06:16 There's only going to be two periods in the first period.

06:19 You're going to have resources and you're going to have uses.

06:22 In the second period.

06:23 Again, you're going to have resources and you're going to have uses.

06:27 So what we call these our budget constraints, our first period and second period budget constraints, your uses are constrained by your resources. So in the first period you're going to have this term A, that's initial wealth. So where does that come from? Well, you can use your imagination.

06:45 It's dropped out of helicopters from the sky.

06:47 You just have a certain initial amount of wealth.

06:50 You also earn an income in the first period y one.

06:54 So those are your resources, your uses.

06:57 In the first period, you can consume that C one or you have b b is going to be your wealth that you carry between periods.

07:05 It's almost savings.

07:07 If A were equal to zero, it would be savings because then y one minus C one would equal B, but since we have this initial wealth, it's not exactly savings. It's going to be your wealth carried over.

07:20 So then in the second period, what do we have? We have our income.

07:23 In the second period, we have the wealth that we carried over and we have any interest that we earned on that wealth.

07:30 So you'll see one plus R times B one times B that's you getting your wealth back and our times.

07:37 B, that's the real interest that you earned on the wealth that you carried over your uses in the second period.

07:45 It's just consumption.

07:46 You're not going to save any more money because after the second period we assume that you die. That's a little drastic.

07:53 I know, but it's a simplification for the model.

07:56 So if that makes you sad, I apologize.

07:58 But that's the way we're going to set up the model after the second period.

08:01 You die, so there's no reason to save after that point.

08:04 So this is your first period and your second period of budget constraint.

08:08 All right. So let's move forward with the model a little bit so we can combine these two budget constraints into our lifetime budget constraint.

08:17 So we can have one simple equation that we can graph and take a look at the incentives of changes in income and changes in interest rates on our consumption and saving patterns.

08:28 All right. So there's one term in common between these two budget constraints.

08:32 That's our B, that's our B variable, our wealth carried over.

08:36 So what we're going to do is we're going to take the first period of budget constraint and we're going to solve for B, when you solve for B, it's a plus Y one minus C one.

08:46 There you can see it's very close to our savings.

08:48 If A were zero again, B would be our savings.

08:52 Now that we solve for being the first period budget constraint, we're going to take it and we're going to stick it into the second period budget constraint.

09:00 So where do you see the B in the second period of budget constraint? You're going to replace it with what we solved for B in the first period budget constraint, and then we're going to combine it all together.

09:11 So when you do that, what you see is C2 consumption.

09:15 The second period equals Y2 plus one plus R times B which is now a plus Y one minus C1.

09:24 We can rearrange this a little bit so that now we'll have the present value of lifetime resources on the left and the present value of lifetime consumption on the right. So what is this present value term I talk about? Well, let's take a look here.

09:38 So you don't need to discount A or Y one that's already in the present, but a value that you're going to have in the future.

09:47 You need to discount that by the interest rate because to have 1000 in the future, you don't have to have 1000 now because you can earn interest on money.

09:57 You need to have x times the interest.

10:00 Rate equals 1000.

10:02 So x the value that you need now equals that 1000 divided by the interest rate you need.

10:09 Whatever value multiply by that interest rate will give you 1000 in the future. So we turn that into what we call net present value.

10:17 So you'll see the net present value of y two is divided by one plus R, and the net present value of lifetime consumption on the right hand side are uses that see one which is already in present value terms and the discounted C two So you divide that by one plus R or the interest rate.

10:36 All right. So now we have our lifetime budget constraint.

10:39 We have the resources on the left and the use is on the right.

10:44 So now we're ready to move into a graph which sometimes helps make this make sense for everybody. When you put it in graphic terms, something you can look at.

10:53 So here's what it looks like.

10:55 It's downward sloping.

10:56 So we have C two on the vertical axis and we have C one on the horizontal axis. You'll notice the more you spend in the second period, the less you can spend in the first period.

11:06 The more you spend in the first period, the less you, the less you can spend in the second period.

11:12 So we have this line that goes down anywhere along this budget constraint, and that's what that line is.

11:18 It's our budget constraint.

11:19 It's feasible you can spend on any one of those points.

11:23 It's possible we call this guy the super saver up here, the guy that spends nothing, nothing in the first period and saves everything for the second period.

11:31 He's the guy you don't want to hang out with.

11:33 He's never willing to pitch in.

11:34 When you go out to lunch, he's the guy that always forgets his wallet.

11:38 You have the guy c one here.

11:40 He's the party animal.

11:41 He spends it all now and leaves nothing for later.

11:44 He's probably fun, but later on he's probably going to have to come back to you and ask you to pay for lunch.

11:49 All right. Most of us aren't those people.

11:51 Most of us are somewhere in the middle that's due to what we call the consumption smoothing theory or the desire of households to maintain a smooth and balanced level of consumption over time.

12:04 So I'm kind of famous in my classes for what they call the consumption smoothing dance because I try to do a little dance to help them remember, and it kind of goes like this.

12:12 I say, You got to smooth your consumption, so I'm embarrassing myself and doing the dance for you.

12:18 Not quite as dramatically as maybe as I do it for them.

12:21 Maybe we'll do an abbreviated one, but we like to smooth our consumption out over time. All right.

12:27 We want these smooth balance levels.

12:29 We don't like big interruptions to our consumption patterns.

12:32 So now any point inside the budget constraint is possible, but it's inefficient. That would be like you have money left over, you're going to die after the second period, but you don't spend the money.

12:43 That makes no sense.

12:44 So you don't want to be in there.

12:45 You're going to spend all that money.

12:47 It's inefficient to be inside the budget constraint.

12:50 Now, outside, that's not feasible.

12:52 You can't be there.

12:53 Your budget doesn't allow you to get there.

12:55 So somewhere along that budget constraint, we're going to be in that area.

13:01 So now let's take a look what happens if there's a change in income, if you have an increase in income, whether it's in this period, whether it's in next period, the first period or the second period, you're going to see an increase in consumption in both periods.

13:15 That, again, is because we want to smooth out that consumption.

13:19 If we earn more money now, we don't want to spend it all now we want to spend some of it now. We want to save some to spend some later.

13:27 If we earn more money later, we know more money is coming.

13:29 We don't want to spend it all later.

13:31 We want to smooth out our consumption.

13:33 We want to pull some of that consumption forward.

13:36 So we're going to save less.

13:38 That's a parallel shift in the budget constraint to the right.

13:41 So you'll have more consumption in both periods.

13:46 It looks like this.

13:47 So I like to use these arrows.

13:49 I think it makes the most sense when you talk about the two period consumer model.

13:53 So an increase in current income, you're going to see an increase in the first period.

13:57 You have more money now you're going to spend some of it.

14:00 Now you're also going to increase your consumption next period.

14:04 So in order to do that, you need to save some of the money that you make.

14:08 Now, say your boss gives you a $100 bonus right now that would mean you spend 50 of it. Now you save 50 of it to spend 50 of it later if your income is going to go up in the future, well, again, you want your consumption to go up in both periods to smooth that consumption out.

14:28 So your boss says, next period I'm going to give you $100.

14:31 So you're going to save 50 less.

14:33 So you can save 50 now and then you're going to spend 50 more later as well.

14:38 So you're going to increase your consumption in both periods.

14:41 In order to do that, you need to decrease your savings again.

14:45 Your savings is your current consumption, your current income minus your current consumption. Why one minus C1? What you see is when Y two goes up, there's no change in y one, but there's an increase in C1.

14:58 So savings will go down.

15:01 So those are your income effects.

15:05 Now let's talk about a change in the real interest rate.

15:08 Now, when there's a change in the real interest rate, it gets a little more complicated. The real interest rate is actually the slope of this line. It's the slope of the budget constraint.

15:18 If there's an increase in the real interest rate, what you're going to see is the slope of that line is going to get steeper.

15:26 As there's an increase in the real interest rate, there's an incentive to substitute away from C one towards C two.

15:35 So we'll talk a bit more about that in a second.

15:37 But right here at this point, this point is, you know, borrowing and no lending point.

15:41 So that says if you spend everything you have in the first period, your wealth and your income in the first period, you save nothing and you just spend everything you earn in the second period, your second period income in the second period.

15:55 So if that's the case, it doesn't depend on the real interest rate.

15:58 Every other point along that line does.

16:01 Every other level of consumption depends upon the real interest rate.

16:05 So the real interest rate represents the opportunity cost of consuming now in terms of foregone consumption in the future.

16:14 So again, opportunity cost, that's the cost.

16:17 Those are the costs you give up in order to do something.

16:20 Whatever you give up in order to do something, those are your opportunity costs.

16:25 So let's say that one more time, the real interest rate is your opportunity cost of consuming now in terms of foregone consumption in the future.

16:34 So if you have $100 and the real interest rate is 10%, if you spend that $100 now, you're going to miss out on $110 of consumption in the second period.

16:44 You get your $100 back and you get the 10% interest.

16:49 So as the interest rate goes up, you have more incentive to save now, consume less now so that you can consume more later.

16:58 So you see that line gets steeper, it moves away from C one and it moves towards C two.

17:05 So if we take a look at our arrows, put it in arrow form again, as the real interest rate goes up, consumption in the first period goes down, consumption in the second period goes up, and we save more money.

17:17 We get a higher return on our savings, so we save more money.

17:23 All right. So we also have what's called the wealth effect.

17:25 When there's a change in the real interest rate, it depends on the type of person.

17:30 All right. Whether you're a net borrower or whether you're a net saver, a net borrower, that's somebody who has liabilities greater than assets.

17:38 You owe money to the bank, say, more than they owe you.

17:41 So you owe them more on a loan than you have in your savings account.

17:45 Well, you pay real interest on that loan.

17:49 So as the real interest rate goes up, you're effectively poorer.

17:52 If you're effectively poor, you're going to spend less money, not in one period, but both periods, because again, we want to smooth out our consumption.

18:01 So see one and see two are going to go down for the net borrower.

18:05 Your savings are going to go up.

18:07 You're going to save more of your income in order to pay off your loan.

18:12 Again, savings is Y one minus C, one y one's not changing here. C one is going down.

18:19 So savings is going up.

18:21 Now a net saver, that's somebody the bank owes the person more than they owe the bank.

18:26 They have they have assets greater than their liabilities.

18:29 Maybe somebody that's further on in life and has, say, $1,000,000 sitting in the bank and the interest rate doubles.

18:36 Well, now his wealth sitting in the bank is accumulating at a faster rate. He's effectively richer.

18:43 So he's going to consume more and.

18:45 Both periods to smooth out US consumption.

18:48 That means the savings are going to go down.

18:50 Why? One isn't changing.

18:52 He's not making more money at work, but his wealth is growing.

18:56 So as wealth is growing, you say, Hey, I don't need to save this money I'm making.

19:00 I'm going to go out and buy myself fancy cars.

19:02 I don't need to worry about it. I don't need to save for retirement.

19:05 So why one minus C one is going to go up or I'm sorry, y one minus C one is going to go down.

19:11 I apologize. Savings will decrease.

19:15 All right. Now, we also have what's called the net effect.

19:18 So the net effect is just a combination of the substitution effect and the wealth effect for a change in the real interest rate.

19:27 So you've already done all the work from this.

19:29 This should be easy for you.

19:30 Now you just combine the effects from the substitution effect and the wealth effect.

19:35 So let's take a look at it for the net borrower.

19:37 When there's an increase in the real interest rate from the substitution effect.

19:41 You want to consume less in the first period for the wealth effect.

19:45 When there's an increase in the real interest rate, the net borrower is poor.

19:49 He wants to spend less in the first period.

19:51 Both arrows are going down from those effects.

19:54 So the net effect, the arrow goes down now for C to the substitution effect for the net, borrower goes up, the wealth effect goes down.

20:04 So we put a question mark without more information, we don't know which effect dominates. So we put that question mark there to say, hey, I don't know.

20:12 All right. For savings in both the wealth effect and the substitution effect, the arrows pointing up, you're saving more.

20:21 So the net effect, we know the net borrower is saving more for the net saver, an increase in the real interest rate.

20:29 It's the same effects as the net borrower for the substitution effect.

20:32 You want to spend less in the first period as the same as the real interest rate goes up. But for the net saver is the real interest rate goes up.

20:41 You want to spend more by the wealth effect, so the arrows are going in opposite directions. So again, we don't know which effect dominates.

20:49 We do know for C2 what's going to happen for both the substitution effect and the wealth effect.

20:55 The net saver wants to spend more in the second period, so the arrow points up for savings for the net saver.

21:04 The arrows are going in opposite directions.

21:06 All right. So for an increase in the real interest rate, he wants to save more by the substitution effect, but an increase in the real interest rate for the wealth effect he wants to save less.

21:16 So it's ambiguous.

21:18 We don't know. So we put a question mark.

21:21 So that is our presentation on consumption and savings.

21:25 Using the two period consumer model, we learned how to define savings.

21:29 We learned why people save.

21:31 We learned about the relationship between savings and consumption.

21:34 We learned how changes in income effect, affect the relationship between savings and consumption.

21:40 And we also learn how changes in the real interest rate affect the relationship between savings and consumption.

21:46 Thank you.