Question

Cindy is a baker and runs a large cupcake shop. She has already hired 11 employees and is thinking of hiring a 12 th. Cindy estimates that a 12 th worker would cost her \(\$ 100\) per day in wages and benefits while increasing her total revenue from \(\$ 2,600\) per day to \(\$ 2,750\) per day. Should Cindy hire a 12 th worker? a. Yes. b. No. c. You need more information to figure this out.

Short answer

Yes, Cindy should hire the 12th worker as it will increase her profit.

Step-by-step solution

Identify the Incremental Costs

First, we determine the additional cost Cindy will incur by hiring the 12th worker. From the problem, we know that hiring this worker will cost her \(100 per day. Thus, the incremental cost is \( \\) 100 \).

Calculate the Incremental Revenue

Next, we calculate the increase in revenue from hiring the 12th worker. The total revenue increases from \( \\( 2,600 \) to \( \\) 2,750 \), which is an increase of \( \\( 2,750 - \\) 2,600 = \$ 150 \).

Compare Costs and Revenue

Now, compare the additional cost of hiring the worker to the additional revenue generated. Since the incremental revenue (\( \\( 150 \)) exceeds the incremental cost (\( \\) 100 \)), hiring the 12th worker increases Cindy's profits by \( \\( 150 - \\) 100 = \$ 50 \).

Conclusion: Decision Analysis

Since the additional revenue is greater than the additional cost, Cindy should hire the 12th worker. This decision would increase her profit by \( \$ 50 \) per day.

Key concepts

Incremental Cost

Incremental Cost refers to the additional cost incurred when a business decides to expand production or increase its workforce. For Cindy, the baker in our example, the incremental cost is directly linked to hiring a 12th worker. When she hires this new employee, she will pay an extra cost of $100 per day, which includes wages and benefits.
Having a good grasp of incremental costs is crucial for any business owner. It helps in determining whether expanding operations or hiring more staff will be financially beneficial. In Cindy’s case, determining this $100 daily cost is a fundamental step to analyze whether the decision to hire will be profitable.
It’s also important to note that incremental cost is not static and can vary based on several factors such as changes in wage rates, labor laws, and operational efficiencies.

Incremental Revenue

Incremental Revenue is the additional income a business earns from taking a specific action, like expanding production or hiring more workers. In our scenario with Cindy, the incremental revenue comes from hiring her 12th worker, which would boost her daily revenue from $2,600 to $2,750. Therefore, her incremental revenue is $150 per day.
Understanding incremental revenue allows businesses to project the expected returns from their investments or operational changes. This helps in assessing whether such decisions are financially viable in the long term.
For Cindy, recognizing that hiring another employee could increase her revenue by $150 daily enables her to weigh this figure against any additional costs, directly impacting her profit margins and business growth.

Profit Maximization

Profit Maximization is a core objective for most businesses, focusing on achieving the highest possible profit from operations. This is done by comparing incremental cost and revenue. The goal is to ensure incremental revenue exceeds incremental cost, thereby increasing overall profits.
In Cindy's case, hiring the 12th worker results in an incremental cost of $100 and an incremental revenue of $150, leading to a profit increase of $50 per day. Cindy's decision becomes clear when she sees that the additional revenue from hiring surpasses the extra expense, making this a profitable move.
Analyzing scenarios to maximize profit involves continuously evaluating operational decisions. It ensures resources are used efficiently, and any potential for profit increase is capitalized upon. Thus, for Cindy, hiring the 12th worker aligns perfectly with her profit maximization strategy.