Utility maximization is a fundamental concept in consumer theory. (a) Explain what is meant by diminishing marginal utility. (b) Assume that a consumer buys only two goods: D and Z. What is the utility-maximizing decision rule for the consumer in allocating total income to good D and good Z? (c) Assume that a utility-maximizing consumer is spending all of her income on the two goods, D and Z. The price per unit of good D is $2, and the price per unit of good Z is $3. The marginal utility of the last unit of good Z consumed is 15. What is the marginal utility of the last unit of good D consumed? (d) Assume that good D is a normal good and good Z is an inferior good. Assume that the consumer's income does not change. Assume that the price of good D increases. (i) Indicate how the substitution effect of the increase in the price of good D will affect purchases of (1) Good D(2) Good Z (ii) Indicate how the income effect of the increase in the price of good D will affect purchases of (1) Good D(2) Good Z