ENGR.ECONOMIC ANALYSIS
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ISBN: 9780190931919
Author: NEWNAN
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Marginal Analysis II Question 1
Assume that a competitive firm has the total cost function:
TC=1q3−40q2+870q+1500TC=1q3-40q2+870q+1500
Suppose the price of the firm's output (sold in integer units) is $700 per unit.
Using calculus and formulas to find a solution (don't just build a table in a spreadsheet as in the previous lesson), how many integer units should the firm produce to maximize profit?
Please specify your answer as an integer.
Hint 1: The first derivative of the total cost function, which is cumulative, is the marginal cost function, which is incremental. The narrated lecture and formula summary explain how to compute the derivative.
Set the marginal cost equal to the marginal revenue (price in this case) to define an equation for the optimal quantity q.
Rearrange the equation to the quadratic form aq2 + bq + c = 0, where a, b, and c are constants.
Use the quadratic formula to solve for q:
q=−b±b2−4ac−−−−−−−√2aq=-b±b2-4ac2a
For non-integer quantity, round up and down to find the integer quantity with the optimal profit.
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