Question

Suppose a person's life is divided into two main blocks, periods 1 and 2. Income in the two periods is equal to y1=100 and y2=100, and taxes are t1=0 t2=100 the comsumers initial weath is equal to 100 . The real interest rate is r = 100%.what is the highest feasible consumption in the furture periods

Answer 1

Lets first form the intertemporal budget constraint.

Period 1 :

c₁ + s = y₁ - t₁ where c₁ = consumption in period 1 , s = saving in period 1

=> s = y₁ - c₁

Period 2 :

c₂ = Saving of period 1 + interest on that saving + Income in period 2 - tax in period 2

=> c₂ = (y₁ - c₁) + r(y₁ - c₁) + y₂ - t₂

=> c₂ = (1 + r)(y₁ - c₁) + y₂ - t₂ where r = 100% = 1

=> c₂ = (1 + 1)(100 - c₁) + 100 - 100

=> c₂ = 2(100 - c₁)

As, the highest feasible consumption in the future periods is that consumption where current period consumption(i.e.c₁) is 0

Thus we have :

c₂ = 2(100 - 0) = 200

Hence, The highest feasible consumption in the future periods is 200.