Assume that an individual consumes three goods, X, Y, and Z. The marginal utility (assumed measurable) of each good is independent of the rate of consumption of other goods. The prices of X, Y, and Z are, respectively, $1, $3, and $5. The total income of the consumer is $65, and the marginal utility schedule is as follows:

a. Given a $65 income, how much of each good should the consumer purchase to maximize utility?

b. Suppose income falls to $43 with the same set of prices; what combination will the consumer choose?c. Let income fall to $38; let the price of X rise to $5 while the prices of Y and Z remain at $3 and $5. How does the consumer allocate income now? What would you say if the consumer maintained that X is not purchased because he or she could no longer afford it?

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Marginal utility of X (units) Marginal utility of Y (units) Marginal utility of Z (units) Units of good 1 12 60 70 2 11 55 60 3 10 48 50 4 40 40 5 8 32 30 7 24 25 7 6 21 18 8. 5 18 10 9. 4 15 3 10 3 12 1