Question

Frank is a single-father with one child. The cost of child-care is equivalent to $150 per day. When Frank works, he receives anhourly wage of $20. In addition he has $150 of non-labor income per day. He sleeps 8 hours a day. Given these constraints, Frank chooses not to work.(a)Suppose now that the government wants to guarantee a $100 daily income level for single-parents who work(i.e., the government subsidizes the gap between $100 and the daily earnings). Draw in a unique diagram (clearly labeled) the pre–subsidy and the post-subsidy budget line faced by Frank. Will he be more likely to work after the introduction of the subsidy?

(b)What if the $100 subsidy is phased out linearlyso thatthe value of the subsidy is $100 if earned income is $0, and it is equal to $0 when earned income is equal to $250? Draw in a unique diagram (clearly labeled) the pre-subsidy and the post-subsidy budget line faced by Frank. Will he be more likely to work after the introduction of the subsidy?

Answer 1

Let number of hour worked by Frank=x

Case1: Budget line pre subsidy

Income=20*x+150

Case2: Budget line post subsidy

Income=20*x+250

Case3: Budget line post subsidy, when subsidy is phased out linearly

Subsidy=100*((250-Income)/250)

Income=20*x+150+subsidy

Income=20*x+150+100*((250-Income)/250)

2.5*Income=50*x+375+250-Income

Income=33.33*x+416.67