9- intertemporal choice problem

Question 1

what is the future value?

Answer 1

the future value shows how much an asset is expected to be worth in the future, if you save M now, you will have M(1+r) at the start of the next period

Question 2

what does the present value show?

Answer 2

Present value shows how much a future asset worth now.
You can think of it as how much money would have to be saved now, in the present, to obtain amount of money 𝑀 at the start of the next period? ⇒ you need to save 𝑀/(1+𝑟) now to have 𝑀 tomorrow.

Question 3

what is the equation of the intertemporal budget constraint?

Answer 3

c2= M2 + (M1 - c1)*(1+r) where c2 is consumption in period 2 , M2 is income in period 2, M1 is income in period 1 and c1 is consumption in period 1, (1+r) is the interest rate

Question 4

what is the optimal consumption choice for the intertemporal choice problem?

Answer 4

maximise U=c1*c2 subject to the constraint c1 + c2/(1+r) =M1 + M2/(1+r)

Question 5

when does a consumer save?

Answer 5

if the income in period 2 is smaller than the future value of income in period 1 the consumer will save ie M2<M1(1+r)

Question 6

when will a consumer borrow?

Answer 6

a consumer will borrow if the present value of future income is greater than income in period 1

Question 7

what is the modified slutsky equation for consumption in period 2 (C2)

Answer 7

dc2/dp2 = 𝜕h2/𝜕p2 +(M2-c2)*(𝜕c2/𝜕M)
where 𝜕h2/𝜕p2 is negative due to substitution effect

Question 8

what is the modified slutsky equation for c1?

Answer 8

dc1/dp2 = 𝜕h1/𝜕p2 + (M2 -c2) * (𝜕c1/𝜕M)
where 𝜕h1/𝜕p2 is postive due to the substitution effect of cross price change

Question 9

for the case of a saver, what occurs to consumption if both goods are normal?

Answer 9

consumption in period 2 increases, effect on c1 will be ambigous

Question 10

for the case of a saver, what occurs if consumption in period 1 is inferior?

Answer 10

consumption in period 1 decreases and consumption in period 2 increases

Question 11

for the case of a saver, what occurs if c1 is inferior and c2 is normal?

Answer 11

effects on both are ambigous

Question 12

when will savings rise?

Answer 12

savings rises only if c1 falls and that is certain only when c1 is inferior

Question 13

for the case of a borrower, what occurs if both consumption periods are normal?

Answer 13

If both 𝑐1 and 𝑐2 are normal: 𝑐1 will fall, but the effect on 𝑐2 is ambiguous.

Question 14

for the case of a borrower, what occurs if c1 is inferior and c2 is normal?

Answer 14

If 𝑐1 is inferior and 𝑐2 is normal: Effects on both are ambiguous

Question 15

for the case of a borrower, if c1 is normal and c2 is inferior what occurs?

Answer 15

If 𝑐1 is normal and 𝑐2 is inferior: 𝑐1 will fall, and 𝑐2 will rise

Question 16

when will borrowing fall?

Answer 16

when c1 is normal