3. a needy family consisting of a mother and three children currently receives c

Question

3. a needy family consisting of a mother and three children currently receives cash benefits that average $12 per day. The mother of this family is allowed to earn an average of $4 per day before her benefits begin to decline. After that, for each dollar earned, cash benefits decline by 67 cents. Plot the recipients money income-leisure tradeoff (budget) line under these circumstances. Assume that she can find work at $4 per hour. how many hours will she have to work per day before her benefits are eliminated? Assuming that her indifference curves for work and leisure are convex, show her equilibrium allocation of time between work and leisure per day. Show that it is possible to have more than one most-preferred outcome.

Explanation / Answer

cash benefits average = $12 per day

allowed to earn =$4 per day

benefits decline=.67ccents=.67$ on each dollar
she find the work =$4 per hour

.67$ will decline at=1
1$ ...................=1/.67
12$...................=1/.67*12=17.91$

so it clear that if she earn 17.91$ her all benefits will eliminate

to earn 17.91$ she will work=17.91$/4=4.4776 hours

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