Final answer:
The value of the marginal product of the last worker hired by the enterprising uncle at his sandwich shop is $12, and assuming the worker's output meets this cost, their marginal product is three sandwiches per hour to justify their hourly wage of $12.
Step-by-step explanation:
Understanding Marginal Product and Profit Maximization
In the scenario where an enterprising uncle opens a sandwich shop and employs 13 people, we analyze the value of the marginal product of his employees. If each employee is paid $12 per hour and the price of a sandwich is $4, the marginal product of a worker is crucial for determining profitability. The marginal product is the additional output generated by hiring one more worker, which in this case is measured in sandwiches produced per hour.
From our given information, if a worker can make two sandwiches per hour, which are sold for $4 each, the revenue generated per hour is $8. A profit-maximizing firm will hire workers up to the point where the cost of labor (wage) equals the marginal revenue product (revenue generated by an employee's labor). Since employees are paid $12 an hour, the value of the marginal product of the last worker hired must be at least $12 to justify their employment.
To achieve profit maximization, the sandwich shop's employment level depends on the marginal product of the workers and the market wage. If the last worker hired produces enough sandwiches that sell to cover their wage, then profit is maximized. Hence, the value of the marginal product for the last worker should equal their wage of $12, and in this case, that worker's marginal product must be three sandwiches per hour (given that a sandwich sells for $4).