Purchase Solution

Total cost function.

Not what you're looking for?

Ask Custom Question

Assume that a competitive firm has the total cost function:

TC = 1q3 - 40q2 + 810q + 1500

Suppose the price of the firm's output (sold in integer units) is $700 per unit.

Using calculus and formulas (but no tables and restricting your use of spreadsheets to implementing the quadratic formula) to find a solution, what is the total profit at the optimal output level?

Please specify your answer as an integer.

Hint: The first derivative of the total cost function is the marginal cost function.

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.

Use the quadratic formula to solve for q:

For non-integer quantity, round up and down to find the optimal value.

Purchase this Solution

Solution Summary

The expert examines finding the optimal output to maximize profit given a firm's production function.

Solution Preview

Assume that a competitive firm has the total cost function:
TC = 1q^3 - 40q^2 + 810q + 1500

Taking the first derivative gives us:
MC = 3(q)^2 - 80 (q) + 810
Setting equal to MR gives us:
700 = 3(q)^2 - 80 (q) + 810
We want to set this ...

Purchase this Solution


Free BrainMass Quizzes
Pricing Strategies

Discussion about various pricing techniques of profit-seeking firms.

Elementary Microeconomics

This quiz reviews the basic concept of supply and demand analysis.

Economic Issues and Concepts

This quiz provides a review of the basic microeconomic concepts. Students can test their understanding of major economic issues.

Economics, Basic Concepts, Demand-Supply-Equilibrium

The quiz tests the basic concepts of demand, supply, and equilibrium in a free market.

Basics of Economics

Quiz will help you to review some basics of microeconomics and macroeconomics which are often not understood.