Chapter 10- Intemporal Choice

Question 1

Future value

Answer 1

The value next period of $1 saved now

FV=m(1+r)

Question 2

Present value

Answer 2

How much do you need to save today to obtain $11 at the start of period 2

PV=m/(1+r)

Question 3

Intertemporal budget constraint (PV &FV)

Answer 3

FV= c2+(1+r)c1=m2+(1+r)m1
PV=c1+(c2/(1+r))=m1+(m2/(1+r))

Can be rearranged to:
C2=m2+(1+r)(m1-c1)

Question 4

Valuing bonds

Answer 4

A bond pays $x at the end if each year for T years (maturity date) it pays its face value $F

What is the most you would pay for such bond?

PV=x/(1+r)+x/(1+r)^2+…+x/(1+r)^T+F/(1+r)^T

Question 5

Present value if a streak of earnings

Answer 5

M1 +M2/(1+r)+M3/(1+r)^2+…+Mn/(1+r)^(n-1)

Question 6

Intertemporal budget constraint with prices

Answer 6

PV: p1c1+p2c2/(1+r)=m1+m2/(1+r)

FV: (1+r)p1c1+p2c2=(1+r)m1+m2

Max consumption in period 2:
c2=((1+r)m1+m2)/p2

Maximum consumption in period 1:
c1=(m1+(m2/1+r))/p1

Question 7

Slope intercept form of intertemporal b.c

Answer 7

If c1 is consumed in period 1 at price of p1 per unit, leaves (m1,-p1c1)

C2=m2+(1+r)(m1-p1c1)/p2

Rearranged:

C2=(m2+(1+r)m1)/p2 - ((1+r)p1/p2)c1

Question 8

Inflation and b.c

Answer 8

P1/p2=(1+π)
π=.2 means 20% inflation

We lose nothing by setting p1=1, so that p2=(1+π)

Rewriting the b.c

p1c1+((1+π)c2)/(1+r)=m1+m2/(1+r)

C1+((1+π)c2)/(1+r)=m1+m2/(1+r)

Question 9

Slope int. intertemporal b.c with inflation

Answer 9

c1=(((1+r)m1+m2)/(1+π))-((1+r)/(1+π))c1

So the slope is -(1+r)/(1+π)

Question 10

Slope of intertemporal b.c with inflation

Answer 10

Slope: -(1+r)/(1+π)

Can be written as: -(1-ρ)=(1+r)/(1+π)

ρ is known as real interest rate

Question 11

Real interest rate

Answer 11

-(1+ρ)=-1+r/1+π Gives ρ=r-π/1+r

For low inflation rates (π~0), ρ~r-π

Note r is sometimes referred to as nominal interest rate

Question 12

Intertemporal choices

Answer 12

Choices of consumption over time