Intertemporal choice

Choice of consumption over time

What could we say capital represents? (in terms of consumption)

Capital represents the diversion of current consumption towards production and future consumption. You can save money today, which will be loaned out to firms for production and then given back to you for your future consumption. The price that firms pay to get your savings is the interest rate, so this is the price of capital for those firms.

Capital market

Driven by individuals’ savings

Firms take out resources that it uses for production

pools of money that frms can draw on to make investments

“Price” in the demand/supply of capital market?

Interest rate - what a firm has to pay to use your money

The price of consuming today vs. consuming tomorrow - The interest rate is the price of consumption today, because by consuming today, you are foregoing the opportunity to save and get the interest rate. The wage rate is the price of leisure. The inflation rate is percent change in the price level year over year. The depreciation rate will be baked into the interest rate.

Supply of capital

household decisions about how much to save, increasing in the interest rate

Demand for capital

comes from firms with potentially productive investments to make; decreasing the interest rate

Intertemporal choice

- Graph over consumption in period one (C1 on x-axis) and in period 2 (C2 on y-axis).
- Slope of the BC is -(1 + r)
- When r changes, e˙ect on savings depends on relative size of IE and SE

Ways to save/loan to firms?

Bank/bonds/equity or stocks

Corporate bonds and equity are a direct way of supplying money to a firm, which they can use to invest in capital. If you put money in the bank, then the bank will loan money to firms, so indirectly, you are still supplying money to firms. If you put your money under the mattress, then firms will not be able to access it.

Budget constraint with intertemporal choice

I = C1 + C2/(1+i)

Consumption tomorrow is effectively cheaper

Key thing to remember when solving for optimal intertemporal consumption?

Solve for C1 and then take savings as a residual of income minus C1

S* = Y - C1*

Explain the substitution and income effects when the interest rate goes up

When the interest rate goes up, any savings you’re doing is now worth more. You are now effectively richer. When you’re richer, you buy more of everything and you’ll have more first-period consumption. So, the income effect actually works in the opposite direction as the substitution effect - raising your consumption today.

The substitution effect (parallel budget constraint to the original indifference curve) lowers your consumption today & increases your consumption tomorrow.

We do not know which of these effects will dominate, so we do not know whether people will save or consume more in the first period.

For a target saver, what will happen when the interest rate increases?

A target saver saves in order to have a specific amount in the next period. If the interest rate increases, then the target saver can save less and still reach this amount. Therefore, the target saver will save less when the interest rate increases and be able to consume more in the first period.

If the substitution effect dominates, the capital supply curve will be ______-sloping.

If the income effect dominates, the capital supply curve will be….sloping

If the substitution effect dominates, then people will consume less in the first period when the interest rate increases because of the higher price, which will lead them to save more and create an upward-sloping supply curve. If the income effect dominates, then people will consume more in the first period when the interest rate increases because they are richer, which will lead them to save less and create a downward-sloping supply curve.

Why is today’s dollar worth less than tomorrow’s?

A dollar today is worth less than a dollar tomorrow because today’s dollar can be invested and an interest rate can be earned

Need to translate all future dollars into today’s terms in order to compare investment and consumption options

Present value

The value of each period’s payment in today’s terms - each payment is weighed according to how far in the future it is.

PV = FV / (1+r)^t PV = Pn / (1+r)^n

Value of perpetuity

Constant pay of “f” every period forever

PV = f/r

Payment divided by interest rate

Real interest rate

the nominal interest rate “i” minus inflation “pi”

r = i - pi

By definition, the real interest rate is the nominal interest rate minus the inflation rate. The real interest rate gives us how much more we will be able to consume if we save for a year, so it is the interest rate that we truly care about.

Future value

FV = Value of payment x (1+i)*N

Compounding interest - you are saving your savings

Inflation

Percent change in the price level

The inflation rate is the percent change in the price level year over year, which essentially is a measure of how much more expensive goods have become in a given year. In the United States, it is measured by comparing a nearly constant bundle of goods from year to year. This measurement is called the Consumer Price Index (CPI). The real interest rate is not a measure of inflation.

Consumer price index

Cost at a point in time of a given bundle of goods

Nominal interest rate

the interest rate you actually get paid

Chain weighted index

Bundle of goods the CPI measures slowly changes over time

Substitution bias

Substitute for less expensive goods when the price of goods go up; no included in CPI

Technological improvement

Maybe price goes up because quality is better, so not necessary that your utility goes down when prices go up

What factors make the inflation difficult to measure with the CPI?

Since consumers’ consumption habits are changing, the CPI cannot simply keep a constant bundle of goods. Income bias is a term I made up. Substitution bias is a problem, because when the price increases for one good, then people will substitute away from that good (in essence, change their consumption bundle). Technological improvement means that the same good might be more valuable now than it was in the past, so we may be willing to pay more for that good. CPI has trouble measuring the change in the increased value we get for that good.

Why is CPI typically an upwardly biased measure of inflation?

Substitution bias causes the CPI to overstate inflation, because it does not account for the fact that people will buy less of goods that experience increases in price. Technological improvement also causes the CPI to overstate inflation, because it does not account for the fact that people could be getting more value from the same good.

When choosing across time periods, how do you compare different choices that may pay off in different periods?

Highest present value

Compare current value with PV = value / (1+i)^n

How should you compare options over time?

You want to compare like to like, so you should compare the present value of each option. Comparing total payoffs would not account for the fact that you could invest money that you received earlier. Comparing the timing or the interest rate would ignore that the payoffs could be of different quantities.

Net present value

Present value of revenues minus the present value of costs

Companies use the net present value to determine if an investment is worthwhile. Investments generate revenues, but also cost money to initiate. The company must account for the present value of the revenues generated by the investment and the costs of making the investment, so the net present value is the present value of the revenues minus the present value of the costs.

What interest rate should a company use when calculating net present value?

A company should use the rate of return on their next best option, because that is their opportunity cost. If the company invests in the analyzed investment they will not be able to invest in their next best option, so this investment must be better than that option for it to be a worthwhile investment

Present value in perpetuity formula

present value / interest rate

How does your discount rate affect your decision to attend college?

Having a high discount rate makes you less likely to attend college. The costs of attending college are temporally earlier than the benefits of attending college, so a higher discount rate will raise the costs and lower the benefits which makes you less likely to attend college.

According to lecture, why might the government provide tax subsidies for savings?

Tax subsidies for savings will encourage savings, which shifts out the capital supply curve and lowers the interest rate. The lower interest raises the net present value of investments, which leads to more investments. More investments create more capital which grows the economy. Tax subsidies usually involve foregoing revenue rather than raising it.

In a tax-deferred retirement account one must…

Tax-deferred means that taxes are deferred until you take money out of the account. This deferment is essentially an interest-free loan, so it encourages people to save more.

Which of the following is the least risky investment?

The money market account is the least risky investment, because it invests in United States government bonds, and the United States government is very unlikely to default.

Which of the following is most risky investment?

Your own company’s stock is the most risky investment. Stocks generally are more risky than corporate bonds and money market accounts. Your own company’s stock is even more risky because it ties your labor income to your investment income. If the company does poorly, you could be fired and lose money in the stock.