Final exam！
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Individualallocationoftimebetweenleisureandmarketproduction1.pptxIndividual allocation of time between leisure and market labour
I Notation for leisure – market labour tradeoff
Total time = T
Time taken as leisure = l
Time spent in market labour = T – l, market wage rate per unit of time = w
Leisure is a “good”, market labour is a bad.
Why spend time in market labour? To acquire income to purchase market-produced goods, C, with price per unit = p
Opportunity cost of a unit of leisure, in terms of market-produced good?
Quantity of C must be given up to obtain one more unit of leisure is w/p
Monetary cost of reducing market labour by one unit is w.
Amount of C that can be purchased by one unit of market labour = w/p
II Numerical example
Consider time measured in hours
Let T = 16 per day w = $20 per hour p = $10
Then if all time spent in market labour income = $320; this can be used to purchase C = 32
Opportunity cost of a unit of leisure = $20/$10 = 2 units of C
NOTE: scale on vertical axis is adjusted to make change in constraint more clear.
C
32
slope = -2 A: on initial budget line where MRS of C for l = -2
B: on budget line after wage decrease where MRS of C for l =
new “real price” of unit of leisure = -15/10 = -3/2
A (initial choice)
D D: substitution effect of decrease in wage rate on indifference curve through A where
B MRS of C for A =-3/2
(choice after w )
Leisure in hours
l at A 16
(total time T)
Lower intercept on vertical axis = 240, reflects 25% decrease in market wage.
Effects of decline in wage rate
Suppose now that w falls from $20/hr to $15/hr.
This will not affect the maximum time available for leisure (16 hrs), but will reduce the maximum income if all time is spent in market labour: spending all 16 hrs in the market will now generate 25% less income, so wT = 16x15 = 240 rather than 320.
Substitution effect: Move from A-D means l increases and C decreases
Income effect: move from D-B means both l and C decrease.
Overall effect on market labour? Given preferences, income effect is larger (in absolute value) than Substitution effect, so leisure falls and market labour increases. With different preferences, could have increased.
