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Lect02_Budget_Sets

Lect02_Budget_Sets - Budget Constraints Consider a consumer...

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1 Budget Constraints Consider a consumer who lives for one period and enjoys consuming two goods. Suppose the consumer has I dollars of income to spend in this period. Let P 1 denote the price of good 1, let P 2 denote the price of good 2, let X 1 denote the number of units of good 1 purchased and let X 2 denote the number of units of good 2 purchased The Budget Constraint is given by P 1 X 1 + P 2 X 2 < I P 1 X 1 is expenditures on good 1 P 2 X 2 is expenditures on good 2 A consumption bundle is a point (X 1 , X 2 ) The Budget Set or Feasible Set is the set of consumption bundles that are affordable to this consumer Budget Line P 1 X 1 + P 2 X 2 =I or X 2 = I/P 2 - (P 1 /P 2 )X 1 X 1 X 2 Budget Set

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2 Example: I=100, P 1 =2, P 2 =4 Budget Line is 2X 1 + 4X 2 = 100, or 4X 2 = 100 - 2X 1 X 2 = 25 - .5X 1 For the consumer's optimal consumption decision, X 1 and X 2 are choice variables. I, P 1 and P 2 are determined outside the model but influence what is affordable for the consumer. X 1 X 2 25 50 slope = -P 1 /P 2 = -1/2
3 How does the budget constraint and budget set change as income and prices change? Suppose I changes (pure income effect). The slope of the budget line is unaffected. There is a parallel shift in the budget line. The budget line shifts out if I increases and shifts in if I decreases. We can also get a pure income effect if all prices increase or decrease by the same percentage. Example: I = 40, P 1 =2, and P 2 =1. The initial budget line is X

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Lect02_Budget_Sets - Budget Constraints Consider a consumer...

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