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1. Prove by mathematical induction: E/- - a) For every integer b) For every integer & , c) For every integer positive, negative, or zero, 2. notes to Use the information in the class find 3. Let there be only two goods X and Y and let X and y be quantities of the two goods purchased by a consumer. Let Ps and py be the prices of the goods. The consumer cannot spend more than his income 1. . If the consumer's utility function is given by U(x,y)=-1/[(x+1Xy+I)] then the consumer's problem is to max subject to The three quantities P., py , and I are assumed to be positive. Find the point (x*.y*) by solving for y in the budget constraint and substituting the resulting expression into the utility function. The objective is now a function of only one variable x.. Does it satisfy the sufficient conditions for a maximum?

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