1. A firm desires to lower absenteeism by rewarding attendance. The firm currently pays its workers a wage of Z dollars per day. A only two goods in a worker's utility function are money income and days of leisure and both are assumed to be normal goods. The number of days of leisure equals L = 365 - D, where L is number of days of leisure and D is number of days of work. The firm has information which indicates the average number of days worked per year was 210. Some workers worked as many as 250 days per year, whereas others showed up for work as few as 180 days. The firm desires to increase the average to 220 days per year. It attempts to do this by offering the following deal:
Offer a lump-sum annual bonus of B dollars to each worker who works at least 220 days a year.
a. Draw the budget line for the typical worker before the bonus program is implemented.
b. Draw the budget line for the typical worker after the bonus program is implemented.
c. Show the effect of this program on the total days worked by employees who were initially
(i) working less than 220 days per year; (ii) working 220 days or more per year.
d. Will this program necessarily raise the average days worked to 220? Explain.
2. To encourage additional spending on education by local school districts, the state government plans to offer aid. All families are alike in district X and these families determine the amount of money spent on education and on all other programs. Both education and all other programs are normal goods. District X is currently spending $500 per student, and the state would like to increase this amount
to $550 per student. The state is considering two proposals:
I. Lump sum grant 1. The state will pay $50 per child toward educational expenditures if the district spends at least $100 per child (which it does).
II. Lump sum grant 2. The state will pay $50 per child toward educational expenditures if the district spends at least $500 per child.
a. Prior to the implementation of any state proposal, show the optimum point for a representative family.
b. How does each proposal alter the budget line?
c. Using graphs, indicate whether the families in district X are more likely to increase per pupil expenditure (i.e., total per pupil expenditure minus per pupil state aid) under proposal 1 or under proposal 2.
d. Is it possible to determine if total spending on education per pupil (local+ state spending) will be higher under proposal 1 or under proposal 2? Explain.