Unformatted text preview: 25 5 2 20 + 2CV + 2CV + 2CV2 = 25 10 210 (4) (3) (1) (2) 40CV + 2 CV2 = 50 CV2 + 20 CV 25 = 0 b + (b2 4ac)1/2 2a 20 + (400 + 100)1/2 2 20 + 22.36067977 2 2.36067977 2 1.180339887 = CV (5) Why don't we do the "minus" part of the "plus or minus" in the quadratic formula? Since we know that the consumer is made worse off and is being "compensated" for a welfare loss, we know that the CV measure must be positive...so we don't need the negative solution from the quadratic formula! So now that we know that CV = 1.18, we can figure out the demands at point CV by subbing (5) into both (3) and (4) respectively. This gives us the point CV as follows: X = 4 + 2CV 5 X = 4 + 2.36 5 X = 4.472 Y = 5 + CV 2 Y = 5 + 1.18 2 Y = 5.59 Just to be sure, let's check the old utility level to see if the point CV is on the old indifference curve... XY = 25 = 5 [(4.472)(5.59)]1/2 = 24.99848 25 (4) (3) 211 So, to summarize the solution at point CV X = 4.472 Y = 5.59 U=5 CV = 1.18 (same as U1) Thus, an income increase of CV = 1.18 will "compensate" for the welfare loss due to a 25% increase in PX, ceteris paribus. [4] At point EV (using old prices and new utility), we have... MRS = PX PY PX X + PY Y = M + EV U (X,Y) = U2 Applying these general conditions to the problem at hand, we get... Y=1 X X + Y = 10 + EV XY = 20 = 4.47 Solving for our consumer's equilibrium at EV X=Y Subbing (1) into the budget constraint... 2 X = 10 + EV X = 5 + EV 2 Now we use the new utility level to determine EV... XY = 20 = 4.47 XX = X = 20 = 4.47 Thus, X = Y = 4.47 212 (2) (1) So now that we know that X = Y = 4.47, we can figure out the EV by solving (2) for EV as follows: X = 5 + EV 2 4.47 = 5 + EV 2 EV = 0.53 2 So, to summarize the solution at point EV X = 4.47 Y = 4.47 U = 4.47 EV = 1.06 EV = 1.06 (2) (same as U2) Thus, an income decrease of EV = 1.06 will be "equivalent" to the welfare loss due to a 25% increase in PX, ceteris paribus. BOADWAY'S PARADOX If we can calculate welfare measures for all of...
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.
 Spring '10
 sning
 Economics

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