Assume that a competitive firm has the total cost function: TC=1q^3−40q^2+ 740 q+1600 Suppose the price of the firm's ou
Posted: Fri Jul 01, 2022 8:19 am
Assume that a competitive firm has the total cost function:
TC=1q^3−40q^2+ 740 q+1600
Suppose the price of the firm's output (sold in integer units)is $650 per unit.
Use calculus and formulas to find a solution (don't justbuild a table in a spreadsheet as in the previouslesson).
Hint 1: The first derivative of the totalprofit function, which is cumulative, is the marginal profitfunction, which is incremental. The lecture and formula summaryexplain how to compute the derivative.
Set the marginal profit equal to zero to define an equation forthe optimal quantity q.
Rearrange the equation to the quadratic formaq2 + bq + c = 0, where a, b, and c representnumbers.
Use the quadratic formula to solve for q:
For non-integer quantity, round up and down to find the integerquantity with the optimal profit.
Hint 2: When computing the total profitfor each candidate quantity, use the total profit function youdefine (rather than summing the marginal profits using the marginalprofit function).
How many integer units should the firm produce tomaximize profit?
What is the total profit at the optimal integer outputlevel?
q= - b ± √b² - 4 to c 2 a
TC=1q^3−40q^2+ 740 q+1600
Suppose the price of the firm's output (sold in integer units)is $650 per unit.
Use calculus and formulas to find a solution (don't justbuild a table in a spreadsheet as in the previouslesson).
Hint 1: The first derivative of the totalprofit function, which is cumulative, is the marginal profitfunction, which is incremental. The lecture and formula summaryexplain how to compute the derivative.
Set the marginal profit equal to zero to define an equation forthe optimal quantity q.
Rearrange the equation to the quadratic formaq2 + bq + c = 0, where a, b, and c representnumbers.
Use the quadratic formula to solve for q:
- Assume That A Competitive Firm Has The Total Cost Function Tc 1q 3 40q 2 740 Q 1600 Suppose The Price Of The Firm S Ou 1 (3.16 KiB) Viewed 34 times
Hint 2: When computing the total profitfor each candidate quantity, use the total profit function youdefine (rather than summing the marginal profits using the marginalprofit function).
How many integer units should the firm produce tomaximize profit?
What is the total profit at the optimal integer outputlevel?
q= - b ± √b² - 4 to c 2 a