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    • Thread Starter

    I'm a little stumped on part b, if anyone could help out a bit.

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

    So, I know the case of min (x,y) x is equal to y. So in order to maximize the budget and follow the utility function the optimal bundle would be 2.5 each, I think. Problem is the price of X isn't given. So I'm kinda confused about that.

    The budget constraint means that pxqx + pyqy = M. The utility function means that he will demand the same quantity of both shoes, so qx = qy, so pxqx + pyqx = M. You are given that py = 2 and M =10, so pxqx + 2qx = 10. Then qx(px + 2) = 10, so qx = 10 / (px + 2).

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