Eaton Micro 6e Ch05

7/27/2019 Eaton Micro 6e Ch05

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2005 Pearson Education Canada Inc.5.1

Chapter 5

Intertemporal Decision Making

and Capital Values


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Intertemporal Decision Making

Intertemporal resource allocationrelates to allocation of resources topresent and future uses.

The rate of interest paid to borrowmoney is the borrowing rate (ib).

The rate of interest earned onsavings is the deposit rate (id).


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Intertemporal Value Comparisons

Future value (FV) is the value that asum of money invested today willturn into at a point in the future.

Suppose $1000 is invested for oneyear at an interest rate (id) of 10%.

The FV = $1000 (1+id) = $1100.

$1000 invested for 1 year at ainterest rate of 10% will turn into$1100 in one year.


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Future Value Rule

From the example:

1. Choose $1000 received today if idexceeds 10%.

2. Choose $1100 received 1 year fromnow if id is less than 10%.

3. Choose either if id equals 10%.


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Present Value

The present value (PV) is the valuetoday of a sum of money received inthe future.

The PV of $1100 received in one yearis the sum of money you couldexchange today for a payment of

$1100 one year from now (ib=10%).

PV = $1100/(1+ib) = $1000


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Present Value Rule

From the previous example:

1. Choose $1000 payable today if ibexceeds 10%.

2. Choose $1100 payable 1 year from

now if ib is less than 10%.3. Choose either if ib equals 10%.


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Separation Theorem

1. Individuals will choose amongdifferent income streams bychoosing the largest present value.

2. They will choose consumptionexpenditures over time to maximizeutility, given the constraint that the

PV of income does not exceed thePV of consumption expenditures.


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Present Values

Mt is the present value of an incomestream (M0, M1, M2, Mt,).

If you deposit PV, at the end of tperiods you will have PV(1+i)t.

This must equal Mt since PV is thepresent value of M

t

(PV(1+i)t = Mt

).

Therefore: PV = Mt/(1+i)t.


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Present Values

The PV of an income stream:

PV=M0/(1+i)+M1/(1+i)2++MT/(1+i)

T

An income stream with equalpayments forever is a perpetuity.

The present value of a perpetuity canbe approximated as: PV = M/i


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Rates of Return

R = (p1-p0)/p0

Where: R = rate of returnp0= current selling price

p1= future selling price


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The Demand for Consumer Capital

and Complimentary Goods

Capital goods are anything thatyields service over time.

Human capital is human endowments

(skills) that yield service over time.Consumer capital - goods valued not

for themselves but for the services

they provide over time.Reservation price is the maximum

price a person is willing to pay.


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Figure 5.1 The demand for film


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Figure 5.2 The demand for a camera


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Figure 5.3 Reservation prices


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Intertemporal Allocation of

Nonrenewable Resources

Bagwells decisions are how much ofhis 10 000 barrels of oil to pump(sell) in period zero (z0) and period

one (z1).

His goal is to maximize the presentvalue of his oil income where w0 and

w1 are the price of oil in period zeroand period one respectively.


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Intertemporal Allocation of

Nonrenwable Resources

The present value of oil income is:PV = w0z0+ w1z1/(1+i)

Given that z1=10 000-z0 (oil sold in one

period reduces oil sold in the other period).

Substituting gives:PV = 10 000w1/(1+i)+z0(w0-w1/(1+i))


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PV = 10 000w1/(1+i)+z0(w0-w1/(1+i))

Where:

10 000w1/(1+i) is wealth if all oil sold inperiod 1.

z0(w0-w1/(1+i)) is the rate of change inwealth as one more unit of oil is sold inperiod 0 and one less in period 1.

If w0>w

1/(1+i), all oil sold in period 0.

If w0


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Hotellings Law

Assuming that each of a greatnumber of people own a smallportion of total oil supply:

PV=w0z0+ w1z1/(1+i)

If z0 & z1 are positive: w0= w1/(1+i)

Rewriting gives w1= w0/(1+i)

The price of oil rises from one periodto the next at the rate of interest.


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Figure 5.4 The optimal time to harvest


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The Life-Cycle Model

The total available for consumptionin period 1 is: C1=M1+(1+i)(M0-C0).

Rearranging gives the budget line:

C0(1+i)+C1=M0(1+i)+M0Note that -(1+i) is the slope showing

that the opportunity cost of a dollarconsumed in period 0 is (1+i) dollarsin period 1.


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Figure 5.5 An intertemporal budget line


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Figure 5.6 The rate of interest and

the intertemporal budget line


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Figure 5.7 Choosing an

intertemporal consumption bundle


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Figure 5.8 Comparative statics

of a change in income


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Initial Savings and a Rise in the

Interest Rate (Figure 5.9)

In this case there is savings in periodone and initial equilibrium of E.

When i rises, the budget lines swivelsaround the initial endowment at A.

The new equilibrium is at E

(consumption in both periodsincreases).


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of an increase in i part 1


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Initial Savings and a Rise in the


For consumption in period 1 theincome and substitution effect are

complementary and C1 increases.For consumption in period 0 the

income effect leads to an increase in

C0, while the substitution effect leadsto a decrease. So C0 may rise or fall.


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Initial Borrowing and a Rise in the


Here there is borrowing in period oneand initial equilibrium of E.

When i rises, the budget lines swivelsaround the initial endowment at A.

The new equilibrium is at E

(consumption in period 0 rises andconsumption in period 1 falls).


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of an increase in i part 2


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Eaton Micro 6e Ch05

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