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# chp5 - ECON 300B Lei Intermediate Microeconomics Winter...

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Unformatted text preview: ECON 300B Lei Intermediate Microeconomics Winter 2011 1 Chapter 5 Chapter 5 Chapter 5 Chapter 5 - Applying Consumer Theory Applying Consumer Theory Applying Consumer Theory Applying Consumer Theory Price Price Price Price-consumption curve and demand curve consumption curve and demand curve consumption curve and demand curve consumption curve and demand curve Consider two goods, x and y. Recall from chapter 4 that when price of good x decreases, the budget line shifts outward. Suppose g G,¡ < g G,¢ < g G,£ , then: The optimal consumption bundle is different at each budget line. They are labeled as ¤ £ , ¤ ¢ and ¤ ¡ respectively in the graph below. If we connect the points ¤ £ , ¤ ¢ and ¤ ¡ , we obtain the ____________________________________________________ . The optimal bundles contain the optimal quantities of good x - ¥ £ ∗ , ¥ ¢ ∗ and ¥ ¡ ∗ respectively. In a separate graph of x against p x , we can plot the points ( ¥ £ ∗ , g G,£ ), ( ¥ ¢ ∗ , g G,¢ ) and ( ¥ ¡ ∗ , g G,¡ ). Joining the points traces out the ______________________________ of good x because it tells the relationship between the price of good x and the optimal quantity demanded of good x. When the price of good x decreases, holding constant the price of good y, good x becomes relatively cheaper. The consumer substitutes good x for good y so quantity demanded of good x increases. Thus, the law of demand holds and the demand curve must be ________________________________________________________ . 1 The two graphs can be stacked up because the horizontal axes both measure level of x. This way, the connection between the price-consumption curve and the demand curve can be seen clearly. 1 A good that does not obey the law of demand (a good that has upward-sloping demand curve) is called a Giffen good. ¦/g G,£ ¦/g G,¢ ¦/g G,¡ § ¥ ¦ g ¨ ECON 300B Lei Intermediate Microeconomics Winter 2011 2 Example Example Example Example In the example of apples and oranges in chapter 4, if g G , g ¡ and ¢ are not given as constants but kept as exogenous variables: £¤¥ ¦G,¡§ ¨©ª,«¬ = uª« s.t. g G ª + g ¡ « = ¢ ℒ = uª« + ­©¢ − g G ª − g ¡ «¬ NFOCs: ℒ G = 1 2 ©ª«¬ ®¯.° « − ­g G = 0 1 2g G ± « ª ² ¯.° = ­ …©1¬ ℒ ¡ = 1 2 ©ª«¬ ®¯.° ª − ­g ¡ = 0 1 2g ¡ ± ª « ² ¯.° = ­ …©2¬ ℒ ³ = ¢ − g G ª − g ¡ « = 0 g G ª + g ¡ « = ¢ … ©3¬ ©´µ¶·¸¹ º»¼½¹¾¤¿¼¹¬ ¥ À ¢ g Á ¸ Â ¸ Ã ¸ Ä x ∗ Ã x Ä ∗ x ∗ Â g Å g Å,Â Æ Â Æ Ã Æ Ä x ∗ Ã x ∗ Ä x ∗ Â ¥ g Å,Ã g Å,Ä Ç g¾¿º¸ − º»¼½µÈg¹¿»¼ ºµ¾É¸ ¨ Ä ¨ Ã ¨ Â ECON 300B Lei Intermediate Microeconomics Winter 2011 3 Substitute (2) into (1): 1 2g G ¡ ¢ £ ¤ .¥ = 1 2g ¦ ¡ £ ¢ ¤ .¥ ¢ = g G g ¦ £ …§4¨ Substitute (4) into (3): g G £ + g ¦ g G g ¦ £ = © £ ∗ = © 2g G is the demand function for apples because it expresses the quantity demanded of...
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chp5 - ECON 300B Lei Intermediate Microeconomics Winter...

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