Today we reviewed the concepts of * marginal productivity of labor* and the

*, from the last two classes. We then went on to talk about the investment (I) component of GDP: Y = C + I + G + NX.*

**marginal propensity to consume**There are two ways in which economists categorize investments:

- Net vs. gross
- By use

For the **Net vs. Gross** categorization, we differentiate between net investment and gross investment. And, essentially, net investment = gross investment – depreciation. So this type of categorization is useful when we are examining the value of investment in **new capital** and not including the costs of that result from wear-and-tear.

When we categorize investment **by use**, we distinguish between the different places that investment money is going, in the macroeconomy. The NIPA categorizes broadly as: (1) Fixed investment (in durables); (2) Residential construction; (2) Non-residential construction and; (3) Changes in business inventories.

Getting into either of those categorizations in more detail would be more appropriate for an accounting course. We’ll stick to that superficial categorization. What we are really concerned with, is what causes changes in overall investment. That can be summed up broadly into two areas:

- “Animal spirits”
- Real interest rates

The “animal spirits” are the same sort of thing that affect the stock market: optimism results in more investment, pessimism in less. Future expectations of wealth lead to increased investment, and if you expect wealth to decrease, your investment will decrease.

Real interest rates affect investments differently, and the relationship is *inverse* – that is, a higher rate leads to lower investment, and a lower rate will spur investment. One way to remember this is to think of the interest rate as a rate that your bank offers for CDs. If the interest rate increases, you (as a manager of a firm) would prefer to invest in the bank than in an asset. Conversely, if the interest rate decreases, you (as the manager of a firm) would prefer to invest in an asset than in the bank. This is another thing that the stock market and investments have in common.

* Present value* (a new concept) is the value today, of a future revenue. This follows from the fact that we assume that inflation-adjusted money loses value over time. If you receive a $1 today, you should be ready to trade it in for $1.05 a year from now, provided the interest rate is 5%. In other words, the value of $1.05 a year from now, is equal to $1 today, if the interest rates are 5%.

So, for instance, if you are expecting a revenue of $105 from a piece of machinery one year down the line, and the interest rates are 5%, you should not pay more than $100 for it right now. Using the rules of compounding to calculate the revenues from something that come in for more than one year, we get the present value formula:

Over here, *r *is the real interest rate, and *n* is the number years into the future you expect your revenues. For instance, if you expect $130 five years later, how much should you be willing to pay right now, if the interest rate is 5%?

You should not pay more than $101.50 for this particular investment. Now, if the interest rates go up to 6%, and the market price of that particular item is $101.50, and you still expect $130 from that item in five years, then your investment decision would change because:

At a rate of 6%, since the Present Value of that investment is $97.14, and the market price is $101.50, this item is over-priced and you’ll be better off investing in a bank, rather than in that item, even though you are getting a revenue of $130 in five years. In fact, even if you have a $101.50, at the higher rate of 6%, if you invest it in a bank, you’ll end up with:

And since you’ll get a higher return from investing in the bank, it makes more sense to do that.

A little addendum: Most of the times, investments last forever – so there is no real “life” of an investment. In that case, we alter our formula a little, and the present value is given as:

If an investment is going to give us a steady revenue of $10,000 per year forever, and the interest rate is 10%, then we should not pay more than $10,000/10% = $10,000/.1 = $100,000 for that investment. If the rates increase, the present-value decreases, and if the rates decrease, the present-value increases.

**The Bottomline** is that in the macroeconomy, people invest *less* when the rates increase, and invest *more *when rates decrease.

To model the effect of interest rates on investment, we take a look at some historical values. Here is a graph of the level of investment versus the bank loan prime rate, from 1990 to 2007.

Although investment is volatile, we do have a downward trend showing us that as the lending rates increased, investment decreased. In fact they decreased by $83.50 billion, for each percentage point increase in the lending rates. This brings us to a more generalized version of the relationship between investment and the real rates: . Here, I_{0} is the “baseline investment”or anything that affects investment, but is independent of the real rate, and I_{r} is the “investment response to changes in the real rate.”

So, for the figure above, I_{0} = $6,337 billion, and I_{r} = $83.50 billion.

This is where we stopped. Next class, we’ll do a short review of this stuff, and move on to the other components of GDP. Hopefully, we’ll finish up with Chapter 6 by next time.

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