022 Exam 1 Sample A, Problem 9

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Find the marginal cost to produce one more item if the fixed cost is $400, the variable cost formula is , and the current production quantity is 9 units.

Foundations:  
Recall that the total cost, , is the sum of the fixed and variable costs. Also, the marginal cost at units is defined to be the effective cost of the next unit produced, and is precisely .
Solution: 
Note that
The expression of the marginal cost is then
Finally, at a production quantity of 9 units, we have the marginal cost
Hence, the marginal cost at a production quantity of 9 units is $58.
Final Answer:  
The marginal cost at a production quantity of 9 units is $58.

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