(a) Combine the period-1 and period-2 resource constraints into a lifetime resou

Question

(a) Combine the period-1 and period-2 resource constraints into a lifetime resource constraint for the economy.

(b) Using lifetime resource constraint you derived in (a), set up a lifetime Lagrangian for the Social Planner's problem in this two-period economy and characterize the economically-efficient choices of consumption and labor (leisure) in each of the two periods - i.e., derive the FOCs of the Social Planner's problem that describe the economically-efficient choices of c1, c2, n1, and n2, and combine them into appropriate optimality conditions. (Hint: you should obtain two consumption-leisure optimality conditions, and one consumption-savings optimality condition here).

Explanation / Answer

The income in two period is y1 and y2 and consumer can consume in two period only thus the individual can save a part of his income in first period but consumes all his income in period 2. Therefore he can save (y1 - c1) amount in period 1 and earns an interest of r% and consumes this saved income in period 2 along with the entire income of period 2

Thus we have

c2 = (1+r) (y1-c1) + y2

(1+r) (y1-c1) + y2 - c2 = 0 ............. (1)

dividing equation (1) by (1+r) we get

y1-c1 + (y2-c2)/(1+r) = 0

hence proved

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.