Question

1 Elasticity 2. What is special about the elasticity of a Cobb-Douglas utility function? 3. Assume a linear demand curve. Why is the consumer's expenditure maximized where ε = -1?

Answer 1

considering U the cobb dong las utility Auctions AKIK KL. 2 x n o La L1 C урь, Молчi va ush ob - .. | M01 : 20 - 4 x 1 x an and marginal utility of X2 M) MU2 = 20 = A (1-x) x 2 X₂-4 Now, a good budgit suppose Price of and ai is P and Price ne į P2 and income isų m. Hince the constraint will it . My la - M= Pirit P2 K2 (371) Now, utility wianimising condition will be the M01 P MU2 P2 web A 2 x 2-1 Rel-15 -A(1-2) KK X22 27 A 2 H2 P (1x) x1 i P26 vt => WP2 X X ₂ = API (1-2) 12 ) => 1 on 1 Pi (1-x) x 1 DE PLQ Now substituting value of x2 in the budget -Constraint we get! cs Scanned with CamScanner

و مرا دید و ... . + A X2 (ص X ) » => emin o Pirit P2X PLARI P24 P یا رمز 1 a2-1م + احط عمره 1) ( 6 ( 1a ) We M - 2 « ) ر و تهران * ماده داریم با ترند: ا (218-M) و (د | " P) (1-4) (": ادر) المسار = دا... اور ان دنا ( رم و 122 ) ل ۴ لا رة ا (هانا ( از 1 دن پی برد ... زد و با برادر زاده ( 1 - 2) M و (= | در (۱) رضSenned w Te

22.2MN2017 2015 P(12)_ 10- forog am not sure who ENER 2 Pili-d) A L SAA wigami Nobel a l _pilla) 18). Svo S w eet home Huce demand for an am NOWdx 2Mb Nu I Now Price elasticity of demaid for u Grad dpi xi substituting dry -- .m and x = 2m NGA 09. 30 We get's a partnerid Lumenso 01. .2 MPI MadalA Hace also leite value of elasticity lElla an - - This is true for Price elasticity of demand for good a also hace, the elasticity of a cobb-Douglas Utility function ii unity. This means that 1% Change in pice level charges quantity by 1% ] cs Scanned with the SamScanner

In a linear demaids bruction such as c - p= a-ba (%) When I E Z 1 ) then the portion of the demand cmuc is inelastic this mean that along this portion, 1.6 en heasc in 1 Price level will cause a less than 1% increase in the quantity sold hence L enpenditure Piqi) in creass caloud the portion where I EL 21 . When El>A => then the portion of the demand cure is clastic. This means that along this portion of 1% increase in Price Elevel will cause a more than 1% decline in the quantity sold. Humie to tal expendistime -(P1q1) decreass along the portion where? LE11. When E=-1 or lel= 1 -> then the portion of the demand ave is unitary elastic. This means that along this porttion, 1 % increase in Price levil will Care an enact 10% decrease in quantity sold. Hence the total enpun ditme CP121) remain unchanged and hence con swier's totul enpuiditime is on I manimised on enpreditme docunt depend on Shall Price change when & ze nog rod went of all okoll told crusan at turu a trods art Milti ollt werd drap and Quel vil mé sorolt Scanned With Canscanner