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ClassNotes - Intermediate Microeconomics The Science of...

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Unformatted text preview: Intermediate Microeconomics: The Science of Choice Dr. Jeremy Petranka UNC - Chapel Hill October 2, 2011 Contents 1 Demand 3 1.1 Demand Curve - Graphical Derivation . . . . . . . . . . . . . . . . . . 3 1.2 Demand Curve - Mathematical Derivation . . . . . . . . . . . . . . . 6 1.2.1 Law of Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Income and Substitution Effects . . . . . . . . . . . . . . . . . . . . . . 9 1.3.1 Graphical Derivation . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3.2 Normal and Inferior Goods . . . . . . . . . . . . . . . . . . . . 13 1.4 Income Effects - Graphical Derivation . . . . . . . . . . . . . . . . . . 19 1.5 Income Effects - Mathematical Derivation . . . . . . . . . . . . . . . . 19 1.6 Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.6.1 General Definition . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.6.2 Demand Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Chapter 1 Demand With the tools we have developed up to this point, we now have the ability to answer the very general question, “with a defined set of preferences and a con- strained set of choices, what will an individual choose?”. This is a very powerful question to be able to answer, and we do so throughout the economics literature to make predictions on human behavior in a variety of scenarios. However, we oftentimes want to expand the question to ask “with a defined set of preferences, how will an individual’s choice change as the world changes?”. For instance, will a government mandate on ethanol fuel-blends cause the price of corn (a com- mon ingredient used to create ethanol) to increase? If so, how will that affect the decisions of lower-income individuals? Could we potentially see a decrease in college education for lower-income individuals due to the fact their increased food budget makes paying for college more difficult? 1 1.1 Demand Curve - Graphical Derivation Consider the preferences represented by Figure 1.1(a). Given an income of $20, a Good 1 price of $5 and a Good 2 price of $4, we can determine the individual’s optimal choice. Using the graphical tools presented in the previous chapters, we know the individual will choose a bundle of (1,4), as shown in Figure 1.1(b). If the price of Good 1 decreases to p 1 = 4, Figure 1.2(a) shows us the individual’s optimal bundle will change to (2,3). If the price of Good 1 decreases to p 1 = 2, Figure 1.2(b) shows us the individual’s optimal bundle will change to (4,3). 1 Anderson and Coble (2010), Hayes (2009), Pimentel (2003), and others discuss the many policy impacts of ethanol usage. 1.1 • DEMAND CURVE - GRAPHICAL DERIVATION | 4 (a) Sample Preferences (b) I = 20, p 1 = 5, p 2 = 4 Figure 1.1: Constrained Optimization Problem (a) I = 20, p 1 = 4, p 2 = 4 (b) I = 20, p 1 = 2, p 2 = 4 Figure 1.2: Constrained Optimization Problem 5 | CHAPTER 1 • DEMAND If we repeated this process for all possible Good 1 prices and plotted the amount...
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This note was uploaded on 02/15/2012 for the course ECON 410 taught by Professor Codrin during the Fall '07 term at UNC.

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ClassNotes - Intermediate Microeconomics The Science of...

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