I have having problems with the first part of the problem. Assume that a welfare

Question

I have having problems with the first part of the problem. Assume that a welfare program pays $100 per week if a person does not work and reduces the welfare benefit dollar for dollar with earnings. Assume that the individuals does not have any other nonwage income. ALso assume the individual has a market wage of $5/hour. Assume maximum of 120 hours of leisure per week (T=120/week)?

What is the break-even level of earnings under the program? What is the breakeven level of hour of work under the program?

the equation I have is S=B-tY, where B=basic benefit, t=benefit reduction rate, Y level of earned income? I . I think that the equation should be 0=100 - 1.00Y and then solve for Y, though I am not sure if thats right because I don't know if thats the right approach to equation?
Please help me thank you

Explanation / Answer

Profit he will earn by working against when he is not working will be 5*H - F where H is the number of hours he works and F is the fixed amount he gets if he does not work. Break even level of earning will be equal to the maximum amount he will be able to earn given his leisure. He has a maximum amount of leisure as 120 hours. Thus the number of hours he can work in a week will be: 168 - 120 = 48 Thus the break even level of earnings will be 5*48 - 100 = 140 In the second part. the break even level of hour of work under the program will be when 5*H = F That is; H = F/5. or 20 hours.

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