Lecture3 - Fin501 FinancialEconomics

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Fin 501 Financial Economics Lecture 3: Utility Maximization, Demand and Elasticities Professor Nolan Miller 1
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Announcements The math review notes are posted on Compass. Problem Set #1 is due on Tuesday, Sept. 7, 2010  ***NOTE CHANGE  IN DUE DATE***. 2
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Last Time … Demand (Graphically) Preferences Rationality Utility Functions Marginal Rate of Substitution 3
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This time … Examples of Utility Functions. Budget Constraints. Utility Maximization Problem. Solving UMP: Demand Functions. Impact of changes in wealth. Impact of changes in prices. Elasticities. Market Demand 4
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5 Examples of Utility Functions Relative sizes of  α  and  β  indicate the  relative importance of the goods. MRS is constant along rays from the  origin. “Homothetic” MRS decreases smoothly. Q of x Q of y
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6 Examples of Utility Functions Perfect Substitutes utility =  U ( x , y ) =  α x  +  β y Indifference curves are linear. One unit of x is always  equivalent to  α / β   units of y. 2-liter bottles and 1-liter bottles. MRS is constant along the  indifference curves. Q of x Q of y
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7 Examples of Utility Functions Perfect Complements utility =  U ( x , y ) = min ( α x β y ) Think of left shoes and right  shoes. Goods are valued in fixed  proportions. There is no substitution  between goods. Q of x Q of y
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8 Constraints on choices Utility functions describe consumers’ preferences. Consumers prefer more to less. Why don’t they choose to have more of everything? They face a budget constraint.
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9 Budget Constraints Let p x  be the price of x and p y  be the price of y. Suppose the consumer has m units of wealth. Then the consumer’s choice must satisfy the Budget Constraint: p x  x + p y  y ≤ m. And, since goods are real, we also require x and y to be non-negative (≥0). If consumers maximize, there is no satiation and no savings, then the  budget constraint should hold with equality.
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10 The Budget Constraint Rearrange the budget  equation to get: y = -p x /p y  * x + m/p y . Slope is –p x /p y . Spend m on x, buy m/p x   units. Sepend m on y, buy m/p y   units. Set of feasible choices in  green. m/p y m/p x Slope = - p x /p y (price ratio) p x x + p y y = m x y
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11 What happens when m increases from  m 1  to m 2? m 1 /p y m 1 /p x p x x + p y y = m 1 x y p x x + p y y = m 2 Note that m is only valuable because larger m’s mean bigger budget sets.   Wealth is not valued/consumed directly.
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What happens when p x  increases from  p x1  to p x2 ? m/p
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Lecture3 - Fin501 FinancialEconomics

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