469-2 - CHAPTER 2 OPTIMAL DECISIONS USING MARGINAL ANALYSIS...

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CHAPTER 2 - OPTIMAL DECISIONS USING MARGINAL ANALYSIS CH 2 is devoted to two important topics that will be the basis for the next 8 chapters: 1. Simple economic model of the private, profit-maximizing firm. 2. Introduction to "Marginal Analysis," important tool for arriving at optimal decision. "Marginal" means "a little more or a little less," and this characterizes the majority of our decisions and is the basis for the next 8 chapters, so understanding the logic of marginal analysis is very important. Examples: How many classes to take each semester? How many children to have? How many cars for a household? How many hours to work? How many stores to open? How many different products to offer? How many programs/classes/majors to offer for UM-F? How much output (Q) to produce? How many acres of corn to plant? How many cows to milk? Example of using Marginal Analysis to locate a shopping mall, page 30, Figure 2.1: Assumptions: 1. Developer will build a mall in a town somewhere along the ocean, between towns A and H, to serve customers primarily in those 8 towns. 2. Number of customers per week can be predicted using market surveys (subject to uncertainty of forecasting) as indicated on page 30. 3. Objective/goal is to locate the mall to MINIMIZE the TTM (Total Travel Miles), assuming that minimizing TTM will MAX ________? One approach to solving the problem would be using "enumeration," or an iterative trial-and-error approach, selecting various locations and computing TTM. For example, we could choose Point X, which is 1 mile west of Town C and calculate TTM = 742.5 miles. We could then choose other locations and calculate TTM. However, this approach does not necessarily guarantee an optimal solution, unless every possible location is considered. Marginal Analysis can identify the optimal site with much less computation and much more certainty. Marginal Analysis (MA): Make small changes and see if a given change improves the ultimate objective. For example, we start by arbitrarily choosing Point X, 1 mile west of Town C. It is not necessary to even calculate TTM at that original location to perform MA. We make a small (marginal) change by moving the location 1 mile to the east, from Point X to Town C, and calculate the CHANGE in TTM. There are 70,000 people living to the east of Point X who are all now 1 mile CLOSER, so TTM is reduced by -70,000 for those people. There are 25,000 people living to the west who would now be 1 mile FURTHER, so TTM is increased by +25,000 for those people. Therefore, the net change in TTM is: -70,000 + 25,000 = -45,000 miles, which is an improvement, and we know that Town C is a better location for a mall than Point X. We could now move further in the same direction to Town D, which lowers TTM by -50,000 miles. Moving to Town E would lower TTM by -12,500 miles. Moving to Town F would INCREASE TTM by +22.5 miles.
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