Question

Pat's wage rate is $6 per hour and she has a maximum of 100 hours per week to allocate between leisure and work. Without any welfare assistance program, Pat chooses to work 37.5 hours per week. a. Suppose Pat is eligible for welfare benefits of $225 per week, but benefits are reduced $1 for every $1 she earns. Draw the budget line (label all relevant values) and indifference curve that represents Pat's maximum utility under these circumstances. b. The structure welfare benefits is now changed. Pat's benefit is $120 per week if she does not work and this benefit is reduced 50 cents for each $1 she earns. Draw a budget line for this new system and an indifference curve that represents Pat's maximum utility given the new welfare system. e. Under which program structure does Pat work more? Explain.

Answer 1

answer:

Pat’s wage rate is $6 per hour and she has a maximum of 100 hours per week to allocate between leisure and work. Without any welfare assistance program, Pat chooses to work 37.5 hours per week.

a) Suppose Pat is eligible for welfare benefits of $225 per week, but benefits are reduced $1 for every $1 she earns. Now this implies when she does not work she receives 225. When she works for 'h' hours, her benefits are '225 - 6h' where 6h is the income earned. However, when h reaches 37.5, she receives no benefit so her income is just $225 at h = 37.5.

Income = Consumption E1 63.5 100 Leisure

See that befor this value of h, the total income is fixed at 225. For example, if h = 20, income earned is 20*6 = 120 but this reduces the benefits by 225 - 120 = 105 so eventually the total income is $225. After h = 37.5, there is no benefit so all the income is earned. We have a kink at h = 37.5

Income = Consumption E2 IC1 IC2 63.5 100 Leisure

She is better off in choosing no work since without working she is earning the same income so she ends up at 100 lesiure hours

b) The structure welfare benefits is now changed. Pat’s benefit is $120 per week if she does not work and this benefit is reduced 50 cents for each $1 she earns. When she works for 'h' hours, her benefits are '120 - 0.5*6h' or '120 - 3h' where 3h is the income earned. However, when h reaches 40, she receives no benefit so her income is just $6*40 = $240 at h = 40. Here we have a kink at = 40

Income = Consumption 600 240 225 IC3 60 63.5 100 Leisure
  

c) We believe that under the second program structure Pat works more because this gives her an encouragement to work slightly greater than 37.5 hours but less than 40 hours.
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