09-03-08 - Econ 302 Intermediate Microeconomic Theory...

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Econ 302: Intermediate Microeconomic Theory Andres Elberg University of Illinois at Urbana-Champaign September 3, 2008 Lecture 3: Preferences September 3, 2008 1 / 46
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Summary from Last Lecture In our last lecture we started studying the theory of the consumer How a rational consumer chooses among alternative combinations of goods Divided the exposition into three stages: 1 Characterization of the constraints facing the consumer 2 Characterization of consumer preferences 3 Optimal choice Lecture 3: Preferences September 3, 2008 2 / 46
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Summary from Last Lecture We described the set of feasible alternatives to the consumer. In a two-commodity world the set of feasible bundles (i.e. the budget set) is given by all bundles ( x 1 , x 2 ) 2 X such that p 1 x 1 + p 2 x 2 & m Lecture 3: Preferences September 3, 2008 3 / 46
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Summary from Last Lecture The budget constraint and the budget set x 2 Budget constraint is p 1 x 1 + p 2 x 2 = m. m /p 2 the collection f ll ff d bl bd l Budget of all affordable bundles. x 1 m /p 1 Set Lecture 3: Preferences September 3, 2008 4 / 46
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Summary from Last Lecture Changes in income New affordable consumption x 2 choices Original and new budge new budget constraints are parallel (same Original bd t slope). budget set x 1 Lecture 3: Preferences September 3, 2008 5 / 46
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Summary from Last Lecture Changes in prices x 2 m/p 2 New affordable choices Budget constraint pivots; slope flattens p 1 ’/p 2 Original bd t from p 1 ’/p 2 to p 1 ”/p 2 p 1 ”/p 2 budget set x 1 m/p 1 m/p 1 Lecture 3: Preferences September 3, 2008 6 / 46
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Summary from Last Lecture Taxes Imposition of sales taxes work just like a change in price Quantity tax: p 1 ! p 1 + t Ad-valorem tax: p 1 ! p 1 ( 1 + τ ) Lecture 3: Preferences September 3, 2008 7 / 46
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Summary from Last Lecture Rationing In the case of rationing, consumption of a good cannot exceed a certain threshold. Suppose consumption of good 1 is constrained to be lower than x 1 . The budget constraint can be written as 8 < : p 1 x 1 + p 2 x 2 & m for x 1 & x 1 x 1 = x 1 for x 1 > x 1 Lecture 3: Preferences September 3, 2008 8 / 46
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Summary from Last Lecture Rationing x 2 m p 2 m x 1 p 1 1 x Lecture 3: Preferences September 3, 2008 9 / 46
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Summary from Last Lecture Rationing You can think of rationing as the limiting case of a penalty imposed on consumption above x 1 Suppose the consumer pays a higher price p 0 1 per unit of the good consumed in excess of x 1 The budget constraint in this case is 8 < : p 1 x 1 + p 2 x 2 = m for x 1 & x 1 p 0 1 x 1 + p 2 x 2 = m + ( p 0 1 ± p 1 ) x 1 for x 1 > x 1 Lecture 3: Preferences September 3, 2008 10 / 46
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Summary from Last Lecture Penalty on consuming above a threshold x 2 m p 2 m x 1 p 1 1 x Lecture 3: Preferences September 3, 2008 11 / 46
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Summary from Last Lecture Rationing The case of rationing is equivalent to a penalty that makes consuming above the threshold prohibitively expensive.
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This note was uploaded on 02/27/2009 for the course ECON 302 taught by Professor Toossi during the Fall '08 term at University of Illinois at Urbana–Champaign.

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09-03-08 - Econ 302 Intermediate Microeconomic Theory...

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