In this problem total consumer surplus cannot be computed because the demand curves are asymptotic to the price axis and the required integrals do not converge. Does this matter? Loss of Consumer Surplus from a Price Rise These ideas can be illustrated with our well-worn example. From Example 5.2 we know that the compensated demand function for X is given by X=hx(Px,Py,V) = VPi (5.50)

so, by Equation 5.49, the welfare loss from a price increase from Px — .25 to Px = 1 is given by change in welfare = VPtdP* If we assume V~ 2 is the initial utility level, this loss (because PY = 1) is given by loss = 4(1)-5 - 4(.25)-5 = 2, (5.52)

which is exactly what we found in Example 5.3—when Px rises to 1, expenditures must rise from 2 to 4 to keep this person from being made worse off. If the utility level experienced after the price rise is believed to be the more appropriate utility target for measuring the welfare loss, then V= 1 (see Example 5.3) and the loss would be given by loss = 2(1)5 - 2(.25)-5 = 1. (5.53)

If the loss were evaluated using the uncompensated (Marshallian) demand function the computation would be inPx

= 0-(-1.39) = 1.39, (5.55)

.25 which does indeed represent a compromise between the two figures computed using the compensated functions.