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lecture4

# lecture4 - Lecture 4 Demand Functions Income and...

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Lecture 4: Demand Functions Income and Substitution Effects

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Key Terms in Lecture Demand Function Normal, Inferior, and Giffen goods Substitution effect and Income effect Individual’s demand curve – Movement along a demand curve (change in quantity demanded) – Shift in demand (change in demand) Demand elasticities !"# price elasticity of demand, !""# income elasticity of demand, and !"""# cross-price elasticity of demand Elastic and inelastic Consumer surplus
Demand Functions The optimal levels of \$ 1 , \$ 2 ,…, \$ % can be expressed as functions of all prices and income – Prices and income are exogenous as the individual has no control over these parameters These can be expressed as % demand functions of the form: \$ 1 * = \$ 1 ( & 1 , & 2 ,…, & % , I ) \$ 2 * = \$ 2 ( & 1 , & 2 ,…, & % , I ) \$ % * = \$ % ( & 1 , & 2 ,…, & % , I )

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Important Property of Demand Functions If all prices and income were doubled, the optimal quantities demanded would not change \$ " ( ’& 1 , ’& 2 ,…, ’& % , ’( ) is the solution of max{u(x 1 ,…,x n )} subject to ’& ) \$ ) *+* ’& % \$ % - ’( – By dividing both sides of the BC by we don’t change it: \$ " ( ’& 1 , ’& 2 ,…, ’& % , ’( ) = \$ " ( & 1 , & 2 ,…, & % , ( )
Changes in Income An increase in income will ./"0’ the budget constraint out in a parallel fashion – Since & \$ / & 1 does not change, (if there is an interior solution) the 234 will stay constant as the worker moves to higher levels of satisfaction This is true b/c, at interior solution, 234 - - & \$ / & 1 A good \$ i for which ! \$ i / ! I " 0 over some range of income is a normal good in that range A good \$ i for which ! \$ i / ! I < 0 over some range of income is an inferior good in that range

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Increase in Income Quantity of \$ Quantity of 1 C U 3 B U 2 A U 1 X and Y are normal goods Quantity of \$ Quantity of 1 C U 3 B U 2 A U 1 X is an inferior good over some income range
Changes in a Good’s Price A change in the price of a good alters the slope of the budget constraint – it also changes the 234 at the consumer’s utility-maximizing choice (for an interior soln.) When the price changes, two effects come into play – substitution effect – income effect

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Changes in a Good’s Price Even if the individual remains on the same
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