Assuming r 025 t 10 t 20 y 100 y 100 write the consumer

Assuming r = 0:25, t = 10, t\' = 20, y = 100, y\' = 100, write the consumers lifetime budget constraint and derive the consumers lifetime wealth. (t\' and y\' are the next period tax and output, respectively.)

Solution

Consumers lifetime budget constraint depicts that a consumer cant spend more than he earns in a lifetime.Thus his budget constraint is

C₁ + (1 + r) C₂ = (Y - t) + (1 + r)(Y^\' - t^\') which states that the future value of consumption in period 1 and 2 is equal to the future value of income in period 1 and 2.

Thus lifetime wealth of the consumer would be

(100 - 10 ) + (1 + .25)(100 - 20)

= 90 + 1.25 * 80

= 90 + 100 = 190.