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MicroCh2[1] - Ch 2 Budget Constraint The economic theory of...

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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 two-good 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 market-set 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
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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. To see this more clearly, consider a case where the consumer changes her choice of both goods from ( x 1 , x 2 ) to ( x 1 ±, x 2 ± ) that just exhaust her income m (where x i ± = x i + x i ).
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