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Elasticity

# Elasticity - Elasticities In this handout we look at an...

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Unformatted text preview: Elasticities In this handout, we look at an important concept in economics, the concept of elasticies. FormallyI it is deﬁned as follower Given a function 2: : ﬂash ...,mn) - a The elasticity of z with respect to m.» = evaluated at the point of interest. a (1) In economics, particuiarly in consumer theory, we usually deal with the following elasticities of demand function: ' ' Given a demand‘function of a: : a: = f(pm,py, m) (2) where m = income 13,- = price of'good i - Own elasticity Pa: 8f = —- —- 3 a Cross elasticity = .131 . 2f. - (4) m 5;)“ to Income elasticity m 6 - :5 ' as (53 where =absainte value of 2:2 i.e., = as when :1: 2 0, : *1 when m < 0. Examples We now consider some examples. First refer back to Handout #9 where we deal with the consumer problem when the utility function has the Cobb-Douglas (0-D) form. maximize may?“ subject to pma: + my: in 55 0:920 0 <1 a<1. We have derived the demand functions for both a: and y, restated below: “la Pu Pa: Now, computing all three elasticities yield: glam; m: I Own elasticity = 2'23; = ohm :1 :r 6P3: I (Pay; 0 Cross elasticity =e £120 :1: pg, 0 Income elasticity 3.8m _m pm Note that the results from C-D utility function are extremely and deceptively simple. The demand function is unit elastic and it doesn‘t depend on the price of the other good, 1;. Do not take this as a general result. This holds for this speciﬁc utility function. Let's now consider a. different utility function and see how different the result Imight be. Consider maximize min{a:,y} subject to page: +pyy = m 56' 2 Dry 2 0 To solve this, note that we want as" = y" always. If that is so, we go to budget constraint and write pzm+pym=m and solve to get: * m :1: = - -. . 7 Pm'i‘py () * m l y = . 8 P1: +Pv () One can verify that - Own elasticity = weevil = We?“ - (oz—ﬁnd = )2 new .( —m j: ._.2.u._ ITI- o e 'c' = E“ -m i! _ Cross last: my I ((—W) (p,+p., P=+Pv ‘ ‘ — E —]-'s——. t 7 0 Income elast1c1t3’ — 3 “1+1,” t. :1 I‘m. 4”"- , A. ’ r l a? '13. an . “an: .t or" ...
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Elasticity - Elasticities In this handout we look at an...

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