Dan's preferences are such that left shoes (good x ) and right shoes (good y) are perfect complements. Specifically, his preferences are represented by the utility function U ( x, y) = minimum {x, y}

(a) Draw several of Dan's indifference curves. Which bundles are at the "kink-points" of these curves?

(b) Assume that Dan's budget for shoes is M = 10 and that the price of a right shoe ispy= 2. Find and draw Dan's demand curve for left shoes (quantity demanded as a function of the price p_x).

Given the shape of indifference curves from part (a), we can't use tangency to find the optimal affordable bundle. Instead, use part (a) to find the second equation that characterizes the location of the optimal bundle on the budget line.

(c) If the price of right shoes decreases to p_y= 1 (income is still M = 10), what is the new demand curve for left shoes? Compare the new demand curve to the previous one and determine whether x and y are complements or substitutes.