Suppose Joe has utility U = min(C/60, L) i.e. Joe must have $60 and an hour...

Suppose Joe has utility U = min(C/60, L) i.e. Joe must have $60 and an hour of leisure to get one util.. By extension $30 and 30 minutes of leisure gives him 0.5 utils and $120 and 2 hours of leisure gives him 2 utils. Further, assume that Joe can make $20/hour at his job and has absolutely no savings. Lastly… assume Joe must sleep 8 hours a day (which counts as neither work nor leisure), but can work and/or leisure up to the remaining 16 hours (with fractional hours of work / leisure allowed as well). Joe is trying to figure out how to spend his day.

Draw Joe’s budget set i.e. draw all combinations of consumption and Leisure Joe can afford.
On a separate graph 2 indifference curves: one showing all points where Joe has 2 utils and another where Joe has 4 utils.
What is Joe’s optimal consumption of Labor and Leisure on this day?

Solutions

Expert Solution

(a) The budget constraint would be , for N be the labor hours, and hence N+L=16, and hence, the budget would be or or . The graph is as below (note that the graph is scaled to look clean).

(b) The two indifference curve would have the equation and .

(c) The corner of the indifference would be at where , which would be the utility maximizing combination, irrespective of price of C and L. Putting it in the budget constraint, we have or or or , and since , we have . These are the utility maximizing combination of affordable C and L. The graph is as below.

Rahul Sunny answered 2 years ago

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