Question

Marvin has a Cobb-Douglas utility function, U=q20.5920.5 his income is Y = $500, and initially he faces prices of P1 = $1 and P2 = $4. If p1 increases from $1 to $4, what are his compensating variation (CV), change in consumer surplus (ACS), and equivalent variation (EV)? Marvin's compensating variation (CV) is $ . (Enter your response rounded to two decimal places and include a minus sign if necessary.) Marvin's change in consumer surplus (ACS) is $ U. (Enter your response rounded to two decimal places and include a minus sign if necessary.) Marvin's equivalent variation (EV) is $ . (Enter your response rounded to two decimal places and include a minus sign if necessary.)

Answer 1

Marvin has a cobb-Dong las utility fonction Us 2, 0.522 0.5 əqi 2q2 Now : Marginal utility good 2, muidu = 0.54,-0.5.2015 Marginal utility of good 2 .. MU? = d = a.s q pis 2 os . Now suppose pile of good 1 = Pil Price of good 2 = P2 and in come = ay Huce budget constraint is a #= P, Q, + P2q2 Now utility maninising condition is s I e MU2 .: =) ..0.59,-0.5 2015 Ois 2,0.57.2015 - = ha aj hPa = Zıp 3). a = q = 911 -- ;). CS Scanned with CamScanner.

and q2P2=qIPI ..=) 22 P2 =21 Now substituting I2 = 21h in the budget constraint we gets utility for ction we auti 4 Uz q,015 qos s) 02.2005 RIA) - U= q (hjois 2)::.00 in) 0.5 = 2;* Subs Khka 4 = 42. P. + и Uои we uk - . U= q 0.5 qois => 0 EL PP 20.5 220.5 =) ja (A) 05. 22 =? 01 P2 -01 = 2* Scanned with CamScanner

Now substituting valus of qit and quito in the budget constraint we geti . y = pi qi* + p q * Los = Syne Pi C OSTR ( A ) U => you a pois p2 0.5 0.7 0,015 P2C.SU =) YM 2 R0.5 p0.5 ♡ : This is the enpendit me functio ' s Now compensating variation is the compm.sation required to restore the paso utility to the leve before the price increase : Now betore Price increase, -Pi = 41, P2 = $4 and income y = $500 Now Substituting Pi= $1 , P2 = $4 and. a. so in the expenditure function to We get! en $500 in the : Y= y #= 2p, ois Poison . => y = 2 (1)015 (4 jos u U = 125 :-) 500 - (2x2). U. CamScania 40 -500 Scanned with;

Now value of enpudique (Y) when p inceasu to $4 ie pi= $4, P2=$4 and . Us 125 will be's : 1 Y: 2P, OSPOSO y = 2(430.5 (4 90164 125 - =) Y = 10,000 hence com Persating variatin = 9 (10,000 - 500) :=99,500 ois U Now enfunditne fuction: 1 Y= 2p, O.S P₂ ois u son i Ý the amont of money Now equivalent variation i 4 taken from a consmes that equals the harm done by the price in wease. Now why Pi increases to $4 ie Pi = $4, P2 =$4 and y = $500 value of as utility 500- 21490151410.50 c) Sở - 80 =) 0 625 Now value of enfundique (Y) at initial price B 1 = 41. j k = $4 and U= 6215 CŠ Scanned with CamScanner

- Now, Y= 20, 015 Rois o : o Yo 2(19015143005 * 62.5 =) Ya 250 Hunces Equivalent variation (500- 250) - $ 250 мою, том 2:1:4маміѕ іѕ dоn & Жан le from equation i) We get? 22= qili substituting this in the budget constraint Yh= P, Q, + P2 Q2 we get? y P= Piqi + P2 X (21/1) =J YA = 2Piqi .=) All y = 21 ... This is the demand for ction for goodı. 2P). : Scanned with: CamScanner

P1 = $ 1 and y = $500 at - Now, 250 mini trial 21-e . at Pi = $ 4, Y- $ 500 500,- soos = 62.5 e = (2x4) ? 21 = demand enuc. draw the Now we can 7 Pi in . en simples Change Change . & consues con omad 74 6215 : 250 smples ... ел 0 Г/ AB<p + H4 , ... Now change in consmes е ACDE T ABCD = (62.500)x(4-1). . Now area of =187.5 Scanned with CamScanner

area of A CDE = £x base x height s x ( 250 - 62.5) *( 4-1) = $ 281.25 Now chage in consmes simples = $ (187.5+28). 25) = $ 468.75 Marvin's compensating vacation (ev). is & 9500.00 Marvin's change in consues surplus (les) is $ 469.75 Marvin's equivalent variation (EV) is $ 250.00 Scanned with CamScanner