Chapter 2: OPTIMAL DECISIONS USING MARGINAL ANALYSIS
1. Review basic mathematics tools including calculus (rules of differentiation, minimization/maximization, and partial derivatives)
2. Illustrate these tools with profit functions and other managerial applications
3. Introduce model of the firm including: demand, total revenue, marginal revenue, profit, marginal profit, breakeven points
NOTE: This is a crucial chapter that introduces several important concepts used in successive chapters. It also illustrates the quantitative problem-solving approach characteristic of this course. Some students may have to review previous algebra and calculus to avoid falling behind.
READING: Up to "constrained optimization" on p. 73.
PROBLEMS: 2,4-9, 14 (14 is tricky; 13 is more abstract and unlikely to be on a test.)
WHAT YOU SHOULD BE ABLE TO DO
1. Understand and handle linear and quadratic relationships: algebra and geometry
2. Find minimum and maximum values (using calculus) of functions
3. Apply the math to problems involving: demand, inverse demand, total revenue, marginal revenue, total cost, marginal cost, profits, marginal profit, and breakeven
EXAMPLE:
Suppose the firm's demand and total cost equations are: Q = 12 - 0.5P and TC = 14 + 4Q.
a. Find the inverse demand equation and the marginal revenue function. Plot both on a graph.
b. Find the firm's marginal cost and plot it on the same graph.
c. Determine the optimal price and quantity. Allso show the solution graphically.
d. Verify that you have found a maximum and not a minimum.
e. Determine the profit and marginal profit functions.
f. Find the optimal price and quantity from the marginal profit function,
g. Suppose the total cost equation is TC = 14 + 4Q +0.5Q2. Find the optimal price and quantity: i) by setting MC = MR, and ii) by setting marginal profit equal to zero.