Suppose a Firm's Total Cost Curve Is TC = 5Q²

question 112

Essay

Suppose a firm's total cost curve is TC = 5Q² + 6Q + 125.
a. Find the firm's marginal cost, average total cost, and average variable cost.
b. Use calculus to find the output level that minimizes average total cost.
c. Show that ATC = MC at this output level.
d. Show that this is the minimum ATC by examining the second derivative.

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Definitions:

Distribution

The arrangement, frequency, or spread of something across a particular area or among a specified group.

Average

A statistic specifying the sum of the values that the items in a class have on a quantitative variable P, divided by the number of items.

Distribution

In logic, refers to the way a term is used in a categorical proposition to apply to all members of its category, also relevant in mathematical operations and probability theory.

Relative Frequency

The ratio of the number of times a specific event occurs to the total number of events.