Bill Katz prefers more of good 1 to less and he prefers less of good 2 to more.Bill has convex preferences.If we draw his indifference curves with good 1 on the horizontal axis and good 2 on the vertical axis, then his indifference curves have positive slope but get steeper as they rise.

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Given Bill's preferences, his indifference curves would actually have a negative slope because he prefers more of good 1 and less of good 2. Convex preferences imply that the curves are bowed inward towards the origin, but the slope of the indifference curves would still be negative due to the trade-off between the two goods where he prefers more of one and less of the other.

Bill Katz Prefers More of Good 1 to Less and He