1. Prove by mathematical induction:
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
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
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