Question

Consider two individuals with endowments of T= 60 hours (per week) of leisure, nonlabour income of Y, and a wage of $7.50 per hour. At this wage, assume that workers are constrained by their employers to work 40 hours per week, or not at all.

a. On a carefully labelled diagram, show the equilibrium for a worker for whom 40 hours is the optimum labour supply and a worker who would like to work 20 hours, but still prefers the 40-hour week to not working. Compare the marginal rates of substitution for these individuals at 40 hours per week.

b. The average part-time wage is $7 per hour, in contrast to $7.50 wage for full-time workers. Using the above model, provide an explanation for this difference in wage rates

Answer 1

a)

Refer the diagram which depicts the income-leisure model, where the horizontal axis represents leisure, and the vertical axis represents income earned as a result of working (foregoing leisure). Leisure is from 0 to 60 hours per week, which is allocated between market & non-market activities.

It is given that Worker A voluntarily opts to work 40 hours per week because his indifference curve (Ua) is tangent to the income constraint. At this point, A uses 20 hours of leisure, & earns income of $300+YN.

Person B who is left to choose freely would opt for 40 hours of leisure & $150+YN of income that is his tangency between his indifference curve (Ub) & the income constraint.

If person B is forced to work 40 hours a week, he will not be at a place where their indifference curve (U’b) is tangent to the income constraint. At the mandatory work level of 40 hours a week, person B is on a lower indifference curve (U’b<Ub).. However, the indifference curve which passes through the full leisure point (U’’b) is lower than both the indifference curve. Therefore, while person B would prefer to work only 20 hours, given the choice of 40 hours of work or not working at all, person B would chose to work 40 hours. For worker B at the point of 40 hours a week, we know that the MRS will be greater than the absolute value of the slope of the income constraint because (U’b) cuts through it. However, person A is tangent and thus, his MRS is equal to the absolute value of the slope of the income constraint.

Hence, it is straightforward to conclude that the MRS for person B is greater than the MRS for person A at the point where 40 hours will be worked.

b)

Coming to contractual part-time, its wages are lower than full time wages. The indifference curve will be flatter at the equilibrium for part time work than is the case for full time work.

If we shift the slope of the part-time constraint up so that it meets the indifference curve for A that maximizes utility as in solution a) which is shown above, we can see that MRS at tangency for full-time is greater than the MRS at tangency for part-time. The above condition means that a person at part-time equilibrium values an hour of leisure less than a person at full-time equilibrium, hence is willing to pay less for an additional hour of leisure by means of foregone wage. This leads into a lower wage as far as the workers choice is cared. To generate lower market wage one will still need to look through the demand side of the labour market, which generates from employers.