# MIT - Principles of Microeconomics - Unit 6. Topics in Intermediate Microeconomics - Lec 22. Capital Supply and Markets II

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PROFESSOR: So today we're going to continue our discussion of capital markets.

If you remember the introduction from last time, what we talked about was we talked about labor as an input and where it came from.

And these lectures are about capitals and input, where it comes from. We talked about the fact that while capital, ultimately, is machines, and buildings, and things like that, what we think about in this course, we're going to think about financial capital and what's behind all the different kinds of capital that businesses use.

We talked about peoples' savings decisions as creating a pool of capital from which businesses draw. And then we talked about present value and the notion of considering the fact that dollars in the future are worth less than dollars today.

So with that as background, what we want to do now is talk about how firms and individuals should make choices over time.

We talked a couple of lectures ago about how firms and individuals make choices when faced with uncertainty. So that was sort of a choice across two different states of the world.

You could get hit by a car.

You could not get hit by a car. Now we'll talk about choices across two different time periods, today versus tomorrow, and how people make those choices.

And the answer is going to be pretty simple following what we did last time, which is whenever you're faced with two choices that pay off at different times, you just want to choose the choice with the highest present value. So if you're faced with two streams of payments, you know that you can't just add them up.

What you need to do is you need to add them up in a way that gets present value.

So, for example, consider the example of a professional athlete who's considering two contracts. One contract pays $1 million today, and one contract pays $500,000 today and $2 million in deferred payments in 10 years. So that's the two contract options facing the player.

If you read it in the newspaper, they would describe this is a $2.5 million contract and this as a $1 million contract. However, the newspaper is wrong, because they haven't accounted for the fact that some of those payments are deferred. So they're worth less.

So how do we compare them? Well, to compare them, we have to take the present value of these two streams. So the present value of the first stream is just $1 million, because it's paid today. So putting it in today's dollars, it's worth $1 million.

The second stream is worth, the present value is $500,000 plus $2 million over 1 plus i to the 10th, because it's being paid in 10 years. And actually here, I'm going to not use i. I'm going to use r for the real interest rate.

Remember last time we talked about how what really matters is the real interest rate, the interest rate you get minus inflation, minus the costs of price increases for goods you have to buy with that interest. So remember we want to use the real interest rate here. So I'll use r now.

So, basically, whether this second contract is a better deal or not depends on what the real interest rate is. So if r equals 5%, then the present value of this second contract is $1.73 million. So that is a good deal. On the other hand, if r equalled 20%, if there's a 20% interest rate as there was back in the late '70s, early '80s, then the present value is $0.82 million. So it's not a good deal.

If you remember the introduction from last time, what we talked about was we talked about labor as an input and where it came from.

And these lectures are about capitals and input, where it comes from. We talked about the fact that while capital, ultimately, is machines, and buildings, and things like that, what we think about in this course, we're going to think about financial capital and what's behind all the different kinds of capital that businesses use.

We talked about peoples' savings decisions as creating a pool of capital from which businesses draw. And then we talked about present value and the notion of considering the fact that dollars in the future are worth less than dollars today.

So with that as background, what we want to do now is talk about how firms and individuals should make choices over time.

We talked a couple of lectures ago about how firms and individuals make choices when faced with uncertainty. So that was sort of a choice across two different states of the world.

You could get hit by a car.

You could not get hit by a car. Now we'll talk about choices across two different time periods, today versus tomorrow, and how people make those choices.

And the answer is going to be pretty simple following what we did last time, which is whenever you're faced with two choices that pay off at different times, you just want to choose the choice with the highest present value. So if you're faced with two streams of payments, you know that you can't just add them up.

What you need to do is you need to add them up in a way that gets present value.

So, for example, consider the example of a professional athlete who's considering two contracts. One contract pays $1 million today, and one contract pays $500,000 today and $2 million in deferred payments in 10 years. So that's the two contract options facing the player.

If you read it in the newspaper, they would describe this is a $2.5 million contract and this as a $1 million contract. However, the newspaper is wrong, because they haven't accounted for the fact that some of those payments are deferred. So they're worth less.

So how do we compare them? Well, to compare them, we have to take the present value of these two streams. So the present value of the first stream is just $1 million, because it's paid today. So putting it in today's dollars, it's worth $1 million.

The second stream is worth, the present value is $500,000 plus $2 million over 1 plus i to the 10th, because it's being paid in 10 years. And actually here, I'm going to not use i. I'm going to use r for the real interest rate.

Remember last time we talked about how what really matters is the real interest rate, the interest rate you get minus inflation, minus the costs of price increases for goods you have to buy with that interest. So remember we want to use the real interest rate here. So I'll use r now.

So, basically, whether this second contract is a better deal or not depends on what the real interest rate is. So if r equals 5%, then the present value of this second contract is $1.73 million. So that is a good deal. On the other hand, if r equalled 20%, if there's a 20% interest rate as there was back in the late '70s, early '80s, then the present value is $0.82 million. So it's not a good deal.

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