Chapter 3 - Marginal analysis for optimal decision making. In this chapter, you will learn to: Employ marginal analysis to find the optimal levels of activities in unconstrained maximization problems; explain why sunk costs, fixed costs, and average costs are irrelevant for determining the optimal levels of activities; employ marginal analysis to find the optimal levels of two or more activities in constrained maximization and minimization problems. | Chapter 3: Marginal Analysis for Optimal Decision McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved. Optimization An optimization problem involves the specification of three things: Objective function to be maximized or minimized Activities or choice variables that determine the value of the objective function Any constraints that may restrict the values of the choice variables Optimization Maximization problem An optimization problem that involves maximizing the objective function Minimization problem An optimization problem that involves minimizing the objective function Optimization Unconstrained optimization An optimization problem in which the decision maker can choose the level of activity from an unrestricted set of values Ex., profit maximization in the long-run Constrained optimization An optimization problem in which the decision maker chooses values for the choice variables from a restricted set of values Ex., optimal . | Chapter 3: Marginal Analysis for Optimal Decision McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved. Optimization An optimization problem involves the specification of three things: Objective function to be maximized or minimized Activities or choice variables that determine the value of the objective function Any constraints that may restrict the values of the choice variables Optimization Maximization problem An optimization problem that involves maximizing the objective function Minimization problem An optimization problem that involves minimizing the objective function Optimization Unconstrained optimization An optimization problem in which the decision maker can choose the level of activity from an unrestricted set of values Ex., profit maximization in the long-run Constrained optimization An optimization problem in which the decision maker chooses values for the choice variables from a restricted set of values Ex., optimal combination of capital and labor given a cost constraint Choice Variables Choice variables determine the value of the objective function Continuous variables Discrete variables Choice Variables Continuous variables Can choose from uninterrupted span of variables Discrete variables Must choose from a span of variables that is interrupted by gaps Net Benefit Net Benefit (NB) Difference between total benefit (TB) and total cost (TC) for the activity NB = TB – TC Optimal level of the activity (A*) is the level that maximizes net benefit Marginal Benefit & Marginal Cost Marginal benefit (MB) Change in total benefit (TB) caused by an incremental change in the level of the activity Marginal cost (MC) Change in total cost (TC) caused by an incremental change in the level of the activity Optimal Level of Activity (Figure ) NB TB TC 1,000 Level of activity 2,000 4,000 3,000 A 0 1,000 600 200 Total benefit and total cost (dollars) Panel A – Total benefit and total cost curves A
