Economists attempt to quantify how useful or satisfying people find goods or services by means of utility functions. Suppose that the utility a particular individual derives from consuming x ounces of soda per week and watching y minutes of television per week is
u(x,y) = 1 − e−0.001x2 − 0.00005y2 .
Further suppose that she currently drinks 80 oz of soda per week and watches 240 min of TV each week. If she were to increase her soda consumption by 5 oz/week and cut back on her TV viewing by 15 min/week, is the utility she derives from these changes increasing or decreasing? At what rate?
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