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 Making 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 3- Choice Variables Choice variables determine the value of the objective function Continuous variables Can choose from uninterrupted span of variables Discrete variables Must choose from a span of variables that is interrupted by gaps 3- 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 3- NB TB TC Optimal Level of Activity (Figure ) 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 0 1,000 600 200 Level | Chapter 3 Marginal Analysis for Optimal Decision Making 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 3- Choice Variables Choice variables determine the value of the objective function Continuous variables Can choose from uninterrupted span of variables Discrete variables Must choose from a span of variables that is interrupted by gaps 3- 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 3- NB TB TC Optimal Level of Activity (Figure ) 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 0 1,000 600 200 Level of activity Net benefit (dollars) Panel B – Net benefit curve • G 700 • F • • D’ D • • C’ C • • B B’ 2,310 1,085 NB* = $1,225 • f’’ 350 = A* 350 = A* • M 1,225 • c’’ 1,000 • d’’ 600 3- 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 3- Marginal Benefit & Marginal Cost 3- Relating Marginals to Totals Marginal variables measure rates of change in corresponding total variables Marginal benefit & marginal cost are also slopes of total benefit & total cost curves, respectively 3- MC (= slope of TC) MB (= slope of TB) TB TC Relating Marginals to Totals (Figure ) • F • • D’ D • • C’ C Level of activity 800 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 – Measuring slopes along TB and TC A 0 1,000 600 200 Marginal .
