Question

Sara earns $200 in the first period and $100 in the second period. She lives in the two-period Fisher model of consumption. Therefore, she can borrow or lend at the interest rate r. considering the two-period Fisher’s model,

a) Write down her intertemporal budget constraint.

b) Assume that She is consuming 150 in the first-period and 160 in the second-period. What is the interest rate?

c) What will happen to Sara’s consumption if the interest rate changes to r=10%. Support your interpretation with a related graph.

d) What will happen to Sara’s consumption if interest rate changes to r=30%. Support your interpretation with a related graph.

Answer 1

a) Let C₁ be the consumption in period 1 and C₂ be the consumption in Period 2. I₁ is the income earned in period 1 and I₂ is the income earned in period 2. Given that r is the interest rate, the consumption in period 2 is equal to income in period 2 plus the savings and the interest earned on the savings in period 1.

That is, C₂ = I₂ + (1+r)(I₁-C₁) => C₁ + C₂/(1+r) = I₁ + I₂/(1+r)

Therefore budget constraint is C₁ + C₂/(1+r) = 200 + 100/(1+r)

b) C₁ = 150, C₂ = 160

Substituting this in budget constraint to find r.

150+160/(1+r) = 200+100/(1+r)

60/(1+r) = 50 =>1+r = 1.2 Therefore, r = 0.2

c) If the interest rate changes to 10%, the the interest that he earns on savings is lesser now. Therefore the consumer would want to save less in period 2 and consume more in period 1.