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Unformatted text preview: been made worse off since it is "equivalent" to a welfare loss. However, a positive value for the EV measure indicates that the consumer has been made better off since it is "equivalent" to a welfare gain. Welfare Position Worse off Better off CV Positive Negative EV Negative Positive Alright! Let's do a numerical example to see how this really works! Consider a consumer with a square root utility function, income of $10 (M = 10), and unit prices (PX = PY = 1). [1] At the initial equilibrium E1, we have the following general consumer equilibrium conditions: MRS = PX PY PX X + PY Y = M 208 Applying these general conditions to the problem at hand, we get... Y=1 X X + Y = 10 Solving for our consumer's initial equilibrium X=5 Y=5 U = XY = 25 = 5 (denoted as U1) [2] Now suppose that PX increases by 25% to PX = 1.25, while everything else remains the same. At the new consumer equilibrium E2, we have the following general consumer equilibrium conditions: MRS = PX PY PX X + PY Y = M Applying these general conditions to the problem at hand, we get... Y = 1.25 X 1.25 X + Y = 10 Solving for our consumer's new equilibrium X=4 Y=5 U = XY = 20 = 4.47 (denoted as U2) Thus, a 25% increase in the price of good X, ceteris paribus, will make the consumer worse off since their utility level falls from U1 = 5 to U2 = 4.47. The consumer's demand for good X falls from X = 5 to X = 4 and their demand for good Y remains the same at Y = Y = 5. [3] At point CV (using new prices and old utility), we have... MRS = PX PY PX X + PY Y = M + CV 209 U (X,Y) = U1 Applying these general conditions to the problem at hand, we get... Y = 1.25 X 1.25 X + Y = 10 + CV XY = 25 = 5 Solving for our consumer's equilibrium at CV 1.25 X = Y X = 4Y 5 Subbing (1) into the budget constraint... 2.5 X = 10 + CV X = 4 + 2CV 5 Subbing (2) into the budget constraint... 1.25 (4/5 Y) + Y = 10 + CV 2Y = 10 + CV Y = 5 + CV 2 Now we use the old utility level to determine CV... XY = 25 = 5 [(4 + 2CV)( 5 + CV)]1/2 = 25 5 2 (4 + 2CV)( 5 + CV) =...
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 Spring '10
 sning
 Economics

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