Question

Both men and women have the following labour supply

L(s)=0.5W

L is the labour supply in hours and W is the hourly wage, including in kind payments.

Judy’s gym has 4 female managers and 2 male managers. She needs each manager to work 8 hours per day.

What is the equilibrium wage required to induce a (male or female) worker to supply 8 hours of work?

Assume that, through a deal that is free to Judy, Judy can provide managers with a spa pass that is worth $30/day to the female managers, but worth only $10/day to the male managers.

How much would Judy need to pay each female manager per day in cash?

How much would Judy need to pay the male manager per day in cash?

that is all information

Answer 1

Equilibrium wage:

The equilirium in the labour market will be achieved at a point where Labour demand is equal to labour supply.

Thus equilirium wage would be determined at the point where Labour demand is equal to labour supply. Judy demands each manager to work 8 hours per day.

Thus equilibrium wage would be determined as, 8=0.5w [since at equilibrium, labour demand = labour supply]

w= $16

Amount that Judy needs to pay each female manager and male manager per day in cash:

Equilirium wage rate is $16 per hour.

Thus total wage per day would be $16 x 8 hours = $128

Now, instead of paying $128 per day in cash to each female manager, Judy may pay a spa pass worth $30/day to each female manager and pay the remaining $98 ($128-$30 = $98) in cash.

Similarly, instead of paying $128 in cash per day to each male manager, Judy may pay $118 per day in cash and may provide a spa pass worth $10 per day to each male manager.