Question

Write down the consumer’s lifetime budget constraint and explain what each of the letters represents.

Answer 1

When consumers decide how much to consume and how much to save, they consider boththe present and the future. There is a trade-off involved in deciding between the current an future consumption.

Let us assume the consumer lives for two periods, 1 and 2, where period 1 represents his/her youth and period 2 represents his/her old age. The real income and consumption levels in both periods are (y₁,y₂) and (c₁,c₂). Given taxes in the two periods are t₁ and t₂ , disposable income levels can be written as ( y₁ - t₁ ) and ( y₂ - t₂ ) respectively. Let r be the real interest rate at which the consumer can lend or borrow. The individual does not receive any bequest, nor does he/she receive any inheritance.

Now if s =(y₁ -t₁ - c₁ ) represents savings in period 1, the consumption in period 2 equals disposable income in period 2, the accumulated savings and interest earned :-

c₂ = ( y₂ - t₂ ) +(1+r) s

or, c₂ = ( y₂ - t₂ ) + (1+r) (y₁ -t₁ - c₁ )

Rearranging the above equation we obtain the lifetime budget constraint of the consumer:

c_{1 +} c₂ / (1+r) = y₁ -t₁ + (y₂ - t₂ ) / (1+r)  

It shows the present value of lifetime consumption equals the present value of lifetime disposable income. Here 1/(1+r) is the amount of present consumption that must be forgone to obtain one unit of future consumption, i.e., it shows the relative price of c₂ in terms of c₁ .