#### Time Allocation, Labour Supply and Labour Markets

Time Allocation, Labour Supply and Labour Markets:

Simple Model of Time Allocation as well as Labour Supply:

1) Assumptions:

• Leisure time as a consumption good that is “purchased” by spending time not working.

• A worker forgoes wages in order to consume leisure as well as the cost of leisure is the amount of foregone wages.

• Specified the ultimate time constraint of 24 hours per day, market wages, and a consumer’s non labour income, we can construct a budget constraint that defines the consumer’s attainable combinations of purchased consumption goods and leisure.

2) Time Allocation Budget Line:

• To maintain a two-dimensional instance that we can graph we lump all purchased consumption goods together and give them a price index ( p ).

• Definitions of variables as well as parameters

C = purchased consumption goods,
p = price index for consumption goods
L = leisure, w= market hourly wage rate, V = non-labor income
H = 24 − L =hours of work

• Budget constraint

pC ≤V + w(24 − L)

cf) Should (V / p) be always positive? If an individual has additional outstanding loans than savings, the interest on the loans would constitute a fixed cost before any consumption goods could be bought (ex) alimony and child support. If the budget equation is satisfied with equality when consumption is zero, leisure can be L = (24w + V)/w. The budget line will leave from the consumption intercept to the leisure intercept. Further leisure is unavailable because of the prior financial commitments.

3) Utility-maximizing choice of consumption and leisure: From the above budget equation, we get C= {(24w+V)/p} − (w/p)L

FOC for the utility maximization is dC/dL= −(w/p) (relative wage or real wage)

4) Mathematical treatment:

Max U(C, L) s.t. pC = V + w(24 − L) ⇒ L = U(C, L) +λ[w(24 − L) +V − pC]

From FOCs of the optimization problem,

5) Comparative Statics of a change in non-labor income Parallel shift of budget line ⇒ pure income effect (DIY!!) Empirically leisure is established to be a normal good.

Example:

• Winning a lottery will change leisure choice
• Change in pension benefit as well as retirement decision
• Inheritance
• Antipoverty policy and labor decision

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