Intertemporal Choice

EXERCISE 01

An individual receives €6,000 today and €4,800 in one year. Borrowing and lending are possible at an annual interest rate of 20%.

A.What is the maximum consumption available today?
B.What is the maximum consumption available in one year?

A.

C_0^{\max}=6{,}000+\frac{4{,}800}{1.20}=10{,}000

Borrow €4,000 against next year’s income; the €4,800 repayment uses all of that income.

B.

C_1^{\max}=6{,}000(1.20)+4{,}800=12{,}000

Save all current income. These are the two intercepts of the intertemporal budget line.

Intertemporal Choice

EXERCISE 02

Jill has $40,000 today and will earn $48,000 next year. She wants to consume $50,000 today. Borrowing costs 20%. Compare borrowing $10,000 with borrowing $15,000 and investing the additional $5,000 in a project paying $12,000 next year.

A.Compare next-year consumption.

A.

C_1^{A}=48{,}000-10{,}000(1.2)=36{,}000

C_1^{B}=48{,}000+12{,}000-15{,}000(1.2)=42{,}000

Investing raises future consumption by $6,000.

Intertemporal Choice

EXERCISE 03

Every project costs $1,000. A has $2,000 and projects returning 11%, 11% and 7%. B has $1,000 and projects returning 11% and 7%. C has $1,000 and projects returning 15% and 12%.

A.Which projects are undertaken without lending?
B.How do lending and borrowing change the allocation?

A.

A takes both 11% projects; B takes its 11% project; C takes its 15% project.

B.

The four funded projects return 15%, 12%, 11% and 11%. C borrows $1,000. One 11% project is displaced; the marginal market rate is 11%, with the marginal investor indifferent.