Lecture_04_Demand - Lecture 4: Demand c & 2009...

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Unformatted text preview: Lecture 4: Demand c & 2009 Je/rey A. Miron Outline 1. Introduction 2. The E/ect of Income on Demands for x 1 ; x 2 : Normal and Inferior Goods 3. The E/ect of Price on Demands for x 1 ; x 2 : Ordinary and Gi/en Goods 4. Substitutes and Complements 5. Examples of Demand Curves 6. Revealed Preference 1 Introduction So far we have developed the model of consumer choice. In this model the consumer chooses a bundle of goods so as to maximize utility subject to a budget constraint. This yields optimal choices. We have also seen that, given preferences, the determinants of those choices are prices and income. The next question is how prices and income a/ect demand. We already have an approximate answer based on EC10. We are going to give more detailed and precise answers over the next couple of lectures. We will analyze the demand functions x 1 = x 1 ( p 1 ; p 2 ; m ) x 2 = x 2 ( p 1 ; p 2 ; m ) 1 This notation means that the quantities of x 1 and x 2 demanded depend on prices and income according to the functions x 1 () and x 2 () . We can see this from the graphs, and, in some cases, from the algebra. This notation might seem confusing at &rst glance since x 1 and x 2 are used in two distinct ways. On the left hand side above, these symbols mean the quantities demanded. On the right-hand side, these are the names of the two functions. An alternative approach would be to write, say, x 1 = g 1 ( p 1 ; p 2 ; m ) x 2 = g 2 ( p 1 ; p 2 ; m ) This would be perfectly acceptable as well, but the notation that uses x in both places is standard. We want to provide comparative static results for these equations; that is, we want to determine what happens to the demands for x 1 and x 2 when prices and income change. 2 The E/ect of Income on the Demands for x 1 and x 2 : Normal and Inferior Goods Given our framework for modeling consumer choices, what can we say about the e/ect of income on demand? To start, we know that an increase in income shifts the budget line out in a parallel way: 2 Graph: Shift Out of the Budget Line Due to an Income Increase ( x 2 = 20 & 2 x 1 ) & > ( x 2 = 30 & 2 x 1 ) 3 4 5 6 7 8 9 10 20 x1 x2 How does this a/ect demand for the two goods? We know for certain that quantity demanded of at least one good must increase; otherwise, you would not be on the new budget constraint. We also normally think that with more income, there should be more demand for both goods. We call this a situation involving normal goods. We can see an illustration of this in the graph: 3 Graph: E/ect of Income on Demand: Normal Goods 4 = x 1 = 2 1 x 1 = 2 2 & > 4 = ( x 1 & 2) 1 = 2 ( x 2 & 2) 1 = 2 x 2 = 8 & x 1 & > x 2 = 12 & x 1 1 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 10 11 x1 x2 As we can see, the demand for both goods has gone up, but this is not the only possibility....
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Lecture_04_Demand - Lecture 4: Demand c & 2009...

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