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Unformatted text preview: 1 Ch 2. Budget Constraint The economic theory of consumers is to answer the question: How does a consumer choose the best bundle of goods she can afford . This chapter will examine how to describe what a consumer can afford ; and the next chapter will explore how the consumer determines what is the best . 2.1 The Budget Constraint In reality, there are many goods to consume, but it is convenient for the time being to consider only the twogood case since we can make use of graphical illustration.  We use X or ( x 1 , x 2 ) to indicate a consumption bundle . For i = 1, 2 , x i denotes the quantity of good i chosen by the consumer.  We use P or ( p 1 , p 2 ) to indicate the marketset prices of both goods. For i = 1, 2 , p i denotes the price of good i .  We use m to denote the consumer&s income used for consumption.  The budget constraint of a consumer requires that the amount of money spent on both goods be no more than her income. That is, p 1 x 1 + p 2 x 2 m (2.1)  A bundle of both goods satisfying this constraint is referred to as an affordable bundle. The set of affordable bundles at P m is called the consumer&s budget set , which includes all points that satisfy inequality (2.1) 2.2 The Budget Line To know better about the properties of the budget constraint, let&s study the budget line (associated with (2.1)) first, which is the set of bundles that cost exactly m : p 1 x 1 + p 2 x 2 = m (2.3) budget set figure 2.1 budget line with slope = 2 1 p p 2 p m x 2 1 p m x 1 2 Given P and m , use eqn (2.3) to derive the horizontal and vertical intercept s ( m / p 1 & m / p 2 ), connecting both intercepts gives you the budget line, as shown in figure 2.1. To achieve this, set x i = 0 in (2.3) to have x j = m / p j (where i j ), meaning that the consumer could buy m / p j units of good j if she spends all of her money m on that good. Change equation (2.3) to a function with x 1 as the independent variable: 1 2 1 2 2 x p p p m x = (2.4) We then know that the slope of the budget line is & p 1 / p 2 , which measure the rate at which the market substitutes good 1 for good 2 because p is set only by the market, not by individual consumers....
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 Spring '09
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