Consider two individuals with endowments of 60 hours per week of leisure, nonlabour income of $Y per week, and a wage of $7.50. At this wage assume that workers are constrained by their employers to work exactly 40 hours per week or not at all.
a. On separate diagrams, show the equilibrium of a worker (A) for whom 40 hours is the optimum labour supply, and a worker (B) who would prefer to work 20 hours per week, but still prefers the 40 hour week to not working at all. Compare the marginal rates of substitution for these individuals at 40 hours per week.
b. Show that the employer can make both itself and worker B better off by instituting lower wages for part time workers and letting them work less (assuming that the firm can hire more part time workers at that lower wage).