Question

Your enterprising uncle opens a sandwich shop that employs 6 people. The employees are paid $12 per hour, and a sandwich sells for $6.

If your uncle is maximizing his profit, the value of the marginal product of the last worker he hired is *blank*, and that worker's marginal product is *blank* sandwiches per hour.

Answer 1

Before coming to the question let's just understand the concept of hiring the optimum number of workers by an example

If Price = $4 and Wage = $10

Workers	Output	Marginal Product	Marginal Revenue Product (Price x MP)		Wage
1	10	10	40	>	10
2	25	15	60	>	10
3	30	5	20	>	10
4	32	2	8	<	10
5	30	-2	-8	<	10

In the above table marginal product is the change in output when additional units are produced, it can also be said that additional units produced by the additional workers.

Marginal Revenue Product is additional revenue generated by additional workers.

Now we have to compare additional revenue by the cost of additional labor if additional revenue is greater than the additional cost we will hire that worker until the additional revenue is equal to additional cost after that additional cost will be higher than revenue.

Hence in this example, we will hire 3 workers

Now coming to the question

If Price = $6 and Wage = $12

Workers	Marginal Product	Marginal Revenue Product (Price x MP)
6	??	??

Now in the above example, we noticed that until marginal revenue product or additional revenue becomes equal to an additional cost (wage) we hire after that we stop hiring

So in this situation, your enterprising uncle is hiring workers such that their wage equals the marginal revenue product.

wage = Marginal revenue product

12 = 12

If marginal revenue product is 12 then the marginal product will be

Marginal Revenue Product = Price x MP

MP = Marginal Revenue Product / Price

MP = 12 / 6

MP = 2

Hence If your uncle is maximizing his profit, the value of the marginal product of the last worker he hired is $12, and that worker's marginal product is $2 sandwiches per hour.