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Suppose that the firm pays its workers $46 per day. Each unit of output sells for $12. How many workers should the firm hire

User Thedjpetersen
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2 Answers

9 votes
9 votes

Final answer:

A firm should hire as many workers as needed until the marginal revenue product of a worker equals the wage rate. Since a worker generates $8 per hour and costs $5.75 per hour, it is profitable to hire workers under these conditions, without an exact number provided due to lack of specific output requirements or constraints.

Step-by-step explanation:

To determine how many workers the firm should hire to maximize profits, we must consider the value a worker generates versus their cost. If a worker produces two widgets per hour and each widget can be sold for $4, the worker adds $8 in revenue per hour. However, since the firm pays workers $46 per day and assuming an eight-hour workday, the cost of labor is $5.75 per hour ($46/8 hours = $5.75). To ensure profit, the firm should only hire workers as long as their marginal revenue product (revenue generated by an additional worker) is greater than or equal to their wage.

Since the worker generates $8 per hour in revenue and costs $5.75 per hour, the firm makes a profit of $2.25 per hour for each worker hired. In this scenario, it is profitable to hire as many workers as needed until the marginal revenue product of the worker equals the wage rate. If additional factors such as diminishing returns come into play, which typically happens as more labor is employed without increasing other factors of production, the number of workers to be hired would be less. However, based on the information provided, we do not have a specific number of units of output required or other potential constraints, so we cannot give an exact number of workers to hire.

User Martheli
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21 votes
21 votes

Solution :

A firm hires labor till a point where the cost of hiring is equal to the value of the additional revenue it produces.

We know ,

the wage rate = cos of hiring an additional worker

the value of the additional revenue that the firm produces = price x (MPI) marginal product of the labor.

Therefore, the firm will hire when :

Wage = value of the additional revenue it generates

Thus, wage = price x (MPI) marginal product of the labor ...........(i)

Therefore, given :

wage of a worker = $ 45

Price = $ 12

So, 45 = 12 x MPI

MPI = 3.8

So the marginal product of employing three days of labor = 25-18/4-3 = 7

Marginal product of employing four days of labor = 30-25/4-3 = 5

So the 4th day produces less revenue than the cost that it generates.

So, the firm should hire 3 workers.

User Jaanus
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