Chapter 3 Optimization Doing the Best You Can

Active Learning Exercises for Chapter 3: Optimization: Doing the Best You Can 1. (Optimization in Levels) Suppose there are three possible airports near your home that you use for a flight to Boston. At the closest airport you find an airfare of $400, the middle airport (the second closest to your home) has an airfare of $325, and you would pay $275 to fly from the furthest airport. Assume you want to take a taxi to the airport and the roundtrip cost to the close airport is $20 and will take 15 minutes. The taxi fare to the second airport is $30 and will take 30 minutes. The taxi fare to the furthest airport is $60 and will take one hour. You have a part-time job where you earn $12 per hour. Create a table similar to Exhibit 3.2 and determine which airport is the optimum for you to use. Solution: The optimum is the airport furthest from your house. Airport Time to Airport Cost of Time Traveling to Airport Taxi Fare Airfare Total Cost: Closest 15 minutes $3 $20 $400 $423 Middle 30 minutes $6 $30 $325 $361 Furthest 60 minutes $12 $60 $275 $347 2. (Optimization in Levels; Comparative Statics) Use all the data from exercise 1 for this problem. Assume you have a next door neighbor who is a lawyer who earns $200 per hour. Create a table similar to Exhibit 3.2 and determine which airport is the optimum for your neighbor to use. Solution: The optimum for your neighbor is the airport that is in the middle (or second closest to your house). Airport Time to Airport Cost of Time Traveling to Airport Taxi Fare Airfare Total Cost: Closest 15 minutes $50 $20 $400 $470 Middle 30 minutes $100 $30 $325 $455 Furthest 60 minutes $200 $60 $275 $535 3. (Optimization in Differences: Marginal Analysis) Use the data from exercise 1 for this problem. Create a table using marginal analysis to confirm that the answer for exercise 1 is the same when marginal analysis is used instead of optimization in levels. Solution: When using marginal analysis you need to add a column to compute the change in the total cost as you move the closest airport to the middle airport. The optimum for you remains the airport that is furthest from your house. Airport Time to Airport Cost of Time Traveling to Airport Taxi Fare Airfare Total Cost: Marginal Cost Closest 15 minutes $3 $20 $400 $423 X Middle 30 minutes $6 $30 $325 $361 -$62 Furthest 60 minutes $12 $60 $275 $347 -$14