The following graph applies to a consumer for whom good x is an inferior good. The price of x falls from p to p', and one of the curves below represents the consumer's (uncompensated) demand curve while the other represents the consumer's compensated demand (or MWTP) curve.
a. Which curve is which? (Explain.)
b. What is it about these curves that makes them intersect at the original price p?
c. Once the consumer has optimized at the new price p', illustrate the new (uncompensated) demand and the new MWTP curve.
d. For curves that have shifted, explain why; for curves that have not shifted, explain why as well.
What will be an ideal response?
b. These curves hold fixed everything other than p. Both hold fixed every price other than p, but the uncompensated demand curve fixes income while the compensated demand curve fixed utility. At the intersection point, utility is fixed on the compensated curve at the level that is attained given the income level that his held fixed on the (uncompensated) demand curve. That's why they intersect.
c. The (uncompensated) demand curve does not shift while the compensated demand (or MWTP) curve shifts to the left and intersects with the (uncompensated) demand curve at the new price p'.
d. The uncompensated demand curve does not shift because income has not changed (nor have any of the prices other than p). The compensated demand curve shifts because utility has changed as a result of the price drop. In particular, utility has increased, which -- when the good is inferior, means that the compensated demand curve shifts in. It crosses the uncompensated demand curve at the new price for the same reason that it originally crossed at the original price.
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