Question

A manager of a factory notices that, on average, when 89 workers show up, the factory produces 1224 packages of product per day. When 90 workers show up, output of the factory is about 1232. Each worker gets paid $225 per day. Fixed costs at the factory are about $2000 per day. What is the marginal cost of each additional package of output when the output is changed from 1224 to 1232?

Answer 1

The marginal cost per additional package when output is increased from 1224 to 1232 packages is $28.125. This is calculated by dividing the additional labor cost of $225 by the increase in output of 8 packages.

Step-by-step explanation:

• The question involves calculating the marginal cost of additional output in a business setting. To determine the marginal cost, we need to look at the change in total costs when production output is increased by a certain amount.
• Here, the factory increases its output from 1224 to 1232 packages, which corresponds to hiring one more worker.
• With each worker costing the firm $225 per day and fixed costs being $2000, the total cost for 89 workers is $2000 + (89 × $225), and for 90 workers, it's $2000 + (90 × $225).
• To calculate the marginal cost, we consider the change in total cost (which is just the additional cost of hiring one more worker since fixed costs do not change) and divide it by the change in output.
• The additional cost is $225, and the increase in output is 1232 - 1224 = 8 packages.
• Therefore, the marginal cost per additional package when increasing output from 1224 to 1232 is $225 ÷ 8, which is $28.125 per package.
• This indicates that each additional package costs more than $28.125 to produce, which is quite a bit higher than the wage of $8 per hour mentioned in the context of a worker's value to the firm.