SUMMARY
The cost function of a firm is defined as C(x) = 300x - 10x² - (1/3)x³. The Marginal Cost Function, derived from this cost function, is MC(x) = 300 - 20x - x². The Average Cost Function is AC(x) = (300x - 10x² - (1/3)x³) / x. The output level where marginal cost equals average cost can be determined by setting MC(x) equal to AC(x) and solving for x.
PREREQUISITES
- Understanding of calculus, specifically differentiation for finding marginal cost.
- Familiarity with cost functions in economics.
- Knowledge of algebra for solving equations.
- Basic grasp of average and marginal cost concepts.
NEXT STEPS
- Study the derivation of Marginal Cost Functions in economic models.
- Learn how to calculate Average Cost Functions using different cost equations.
- Explore methods for finding equilibrium points in cost functions.
- Investigate the implications of marginal cost equaling average cost in production decisions.
USEFUL FOR
Economics students, financial analysts, and business managers involved in cost analysis and production optimization.