Question

Need answer to part b please.

2. Inter-Temporal Labor Supply Imagine an individual who lives for two periods (t = 1,2) and faces a sequence of wages W, W2 that is known with certainty. The individual can borrow and save at an interest rate ofr, and has a discount factor of 0 < 1. Each period, the individual has a total time endowment of T. They do not receive any non-labor income, and they do not start life with any assets. The individual chooses consumption and leisure in each period (C, L, C2, L2) to maximize lifetime utility: (T L2)1+ (T- L) B- 1+ C+ +6 1+n - U (C, L, C2, L2) 2 (1) 1+ 1 < 0,y 2 0, and that 6(1r)= 1 You may assume that > 0, (3 points) (a) Write down the inter-temporal budget constraint faced by the in dividual. Explain the economic meaning of this constraint. (If you don't know this, you can "buy" the answer for 3 points) (4 points) (b) Write down the worker's optimization problem and solve for an expression indicating the optimal ratio of hours worked in period 2 relative to period 1:

Answer 1

Lasou Cin penrodD supplced Li = T-N BC 1&pen'odi (TL)W Ct S C2 (T-L2) WhtS C+) penod 2 elimnang 2nd period: BC in 1. n Si aedin& from the two (T-Lz) We (T-L)W t (3 C C2 (+r) This icetine budrt condt vait of he worker. the Tre relative of tonsumption periDd 2, C2, teTs price onsurpton wy.t penbd C The wox Ver &awer BET-L) Max BT-L L Y tn hodds

egra ngeam problen T-LiW T-LWZ - 1Y 1+ Y Fo C - o > Ci I + Y => W BT-LS Cui=T-Li) CLi: 「入W、=0 => H = ,2 Bs(T-L > H2 142 WI > WI Hz W2