Let's examine this naive approach to utility maximization more closely. Based on her demand curve, if the price for CDs is 10 we would expect our consumer to purchase 7. Suppose she tries to maximize her utility by purchasing 13 instead?

    For each CD she buys beyond the 7th, she still pays 10, but according to her demand curve, D, her marginal willingness to pay, or her marginal utility, is less than 10 for each CD beyond the 7th. She's paying 10 for CDs that are worth less than that to her. If she buys 13 CDs instead of 7 her utility increases only by an amount equal to the blue area, but she pays an amount equal to the blue + magenta area. Buying the extra CDs makes her worse off by an amount equal to the magenta area.

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