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Consider a consumer with income of M = 400 and preferences over some good, X, and all other goods, Y , represented by the utility function U (X, Y ) = 100 ln X + Y . Now let’s compute this consumer’s pre- and post-change Hicksian demand curves. Suppose that the price starts at $4 and goes up to $5. (i) Compute the consumers pre-change utility level. (ii) For any given price, the pre-change Hicksian demand curve must satisfy two conditions. First, the slope of the budget constraint must be equal to the MRS, and second, the new bundle must generate the same level of utility, which is to say, it must be on the original indifference curve. Using these two conditions, compute the Hicksian demand curve defined by the pre-change utility level. [Hint: This is a trick question. It should require very little math.] (iii) Without doing any additional math, graph the inverse Marshallian demand curve and both inverse Hicksian demand curves, mark the compensating and equivalent variation for the price increase from $4 to $5 and explain why they are the same.
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