6.9 Consumer surplus with many goods In Chapter 5, we showed how the welfare costs of changes in a single price can be measured using expenditure functions and compensated demand curves. This problem asks you to generalize this to price changes in two (or many) goods.

a. Suppose that an individual consumes n goods and that the prices of two of those goods (say, p1 and p2) increase. How would you use the expenditure function to measure the compensating variation (CV) for this person of such a price increase?

b. A way to show these welfare costs graphically would be to use the compensated demand curves for goods x1 and x2 by assuming that one price increased before the other. Illustrate this approach.

c. In your answer to part (b), would it matter in which order you considered the price changes? Explain.

d. In general, would you think that the CV for a price increase of these two goods would be greater if the goods were net substitutes or net complements? Or would the relationship between the goods have no bearing on the welfare costs?