Saving and Investment1. Preliminaries2. Stocks and Flows, the Interest Rate, Present Values3. Inter-temporal choice: Irving Fisher4. The Effect of Changes on Income and Interest Rates on Consumptionand Saving5. The Demand for Capital and Investment6. Equilibrium in the Market for Saving and Investment7. Bond Pricing8. Stock Pricing9. Risk and Return10. Efficient Market Theory1Preliminaries• Earlier in the course, when we derived consumer theory, we assumedthat all income must be spent in the current period.• But in reality income can be either spent on consumption in the presentor saved for the future.• There are two common meanings to the word saving1. refraining from consuming all of current output now in order toproduce and consume more in the future.2. the acquisition of new assets.• These two meanings are consistent.• Holding income constant, a household decision on how much to consumeis the same thing as how much to save. This decision is essentially atrade-off between present and future consumption.2• What determines the proportion of income that is consumed by a givenhousehold?• As with most economic analysis of spending decision focus on two fac-tors: prices and wealth. At what rate can households trade-off betweengoods? and how much in total can they buy?For the consumption-saving decision, these factors are:– the price of consuming today as opposed to the future– overall lifetime wealth3A Digression on Stocks and Flows• Variables that are measured per unit time are called flow variables.• Variables that are measured at a point in time are called stock variables.• A classic example is a bath tub with water flowing in from the faucet.the amount of water in the tub at any moment is a stock variable.The units of a stock variable (gallons, in this case) don’t have a timedimension. The rate at which water enters the tub is a flow variable;it’s units (gallons per minute) have a time dimension. In this case theflow equals the rate of change of the stock.• Wealth is a stock variable; the units of (dollars) don’t have a time di-mension. The amount of saving (or dis-saving) per period is a flowvariable. The units which is in (dollars per period) have a time dimen-sion.Wealth tomorrow (dollars) = Wealth today (dollars)+saving today (dollars per day)4The price of consumption today versus the future• The variable which determines how much future consumption is givenup by consumption today is the expected real interest rate.• The book defines the interest rate as the rate at which one can borrowand lend money.• It represents the cost in foregone future consumption of consumingtoday.• Let r denote the interest rate.5Present Values• What is the value today of one dollar a year from now?– It is less than one dollar.• Present value is is the value of payments to be made in the future interms of of today’s dollars or goods.• Example: At an interest rate of 10%, $10,000 today invested for oneyear is worth $10,000 × 1.10 = $11,000. So the present value of $11,000in one year is $10,000 (if the interest rate is 10%).• In general ,PV =future value one period from now1+rPV =future value two periods from now(1 + r)26Inter-temporal Choice: Irving Fisher• But for now let’s venture into theory land where there are no taxes, noinflation, no uncertainty, only two periods.• Again we are talking about a world in which there is no money and nogovernment. Everything is in terms of goods. Prices are flexible andmarkets clear.• Consider an environment in which agents live for two periods:– in period 1 they are young– in period 2 they are old• Might be this week and next week ...7• We assume an individual gets utility from consumption (Ct) in eachperiod. He or she is an utility maximizer so he or she wishes to:maxC1,C2U(C1,C2)• He or she earns income during the time 1 period of Y1and earns incomeduring the time 2 period Y2.• He or she can borrow and lend freely across the two periods at aninterest rate r. During the first period, the agentC1+ S = Y1During the second period, the agent’s budget constraint is:C2= Y2+(1+r)S8• So from the second period budget constraintS =Y21+r−C21+r• Combine the two budget constraintsC1+C21+r= Y1+Y21+r• Note everything in this equation is units of “goods in period 1”. Theterm11+ris relative price of goods between the two periods and convertsthe units from the second period into the first.• This budget line equates the present value of lifetime consumption(PVLC) to the present value of lifetime resources (PVLR).9The agent’s problem• So this individual agent maximizes his/her utility over C1and C2giventhe budget constraint.• The budget line– graph budget line in (C1,C2) space.– if C1= 0, then C2=(1+r)Y1+Y21+r – if C2= 0, then C1= Y1+Y21+r– so the slope of line is −(1 + r): the relative price between consump-tion today and consumption tomorrow.• Where is the optimal level of consumption?– Optimal level of consumption point is where the budget line is tan-gent to an indifference curve.– That’s the highest indifference curve that is possible to reach.– All other points on the budget line are on lower indifference curves– At the optimum, the marginal rate of substitution is equal to themarginal rate of transformation. The marginal rate of substitution(the slope of the indifference curve) is the agent’s willingness to tradeoff consumption from one period to the other. And the marginal rateof transformation is the interest rate.10• Saving is thenS = Y1− C1• If the agent choose a point whereC1<Y1,we say that person is a lender.• If the agent choose a point whereC1>Y1,we say that person is a borrower.11The Effect of Changes in Income and Interest Rates on Consumptionand SavingThe effect on consumption of a change in income (current or future) orwealth depends only on how the change affects the present value of lifetimeresources (PVLR).• An increase in current income (Y1)– Increases PVLR, so shifts budget line out parallel to old budget line.– If there is a consumption-smoothing motive, both period 1 and pe-riod 2 consumption will increase– Then both consumption and savings rise because of the rise in period1 income.• An increase in future income (Y2)– Same outward shift in budget line as an increase in current income– Again, with consumption smoothing, both current and future in-come increases– Now savings declines, since