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Chapter Two Budgetary Constraints Contents Describe budget constraint Algebra Graph Describe changes in budget constraint Government programs and budget constraints Non-linear budget lines Consumption Choice Sets A consumption choice set is the collection of all consumption choices available to the consumer. What constrains consumption choice? Budgetary, time and other resource limitations. Budget Constraints A consumption bundle containing x1 units of commodity 1, x2 units of commodity 2 and so on up to xn units of commodity n is denoted by the vector (x1, x2, … , xn). Commodity prices are p1, p2, … , pn. Budget Constraints Q: When is a bundle (x1, … , xn) affordable at prices p1, … , pn? A: When p1x1 + … + pnxn £ mwhere m is the consumer’s (disposable) income. Budget Constraints The bundles that are only just affordable form the consumer’s budget constraint. This is the set{ (x1,…,xn) | x1 3 0, …, xn 3 0 and p1x1 + … + pnxn = m }. Budget Constraints The consumer’s budget set is the set of all affordable bundles;B(p1, … , pn, m) ={ (x1, … , xn) | x1 3 0, … , xn 3 0 and p1x1 + … + pnxn £ m } The budget constraint is the upper boundary of the budget set. Budget Set and Constraint for Two Commodities Budget Set and Constraint for Two Commodities Budget Set and Constraint for Two Commodities Budget Set and Constraint for Two Commodities Budget Set and Constraint for Two Commodities Budget Set and Constraint for Two Commodities Budget Set and Constraint for Two Commodities Budget Constraints If n = 3 what do the budget constraint and the budget set look like? Budget Constraint for Three Commodities Budget Set for Three Commodities Budget Constraints For n = 2 and x1 on the horizontal axis, the constraint’s slope is -p1/p2. What does it mean? Budget Constraints For n = 2 and x1 on the horizontal axis, the constraint’s slope is -p1/p2. What does it mean? Increasing x1 by 1 must reduce x2 by p1/p2. Bud
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