Kyle's utility function is U = 2.7X +2.7Y, where X is units of good X and Y is units of good Y. What is the marginal utility of good X? O 6 O 3.7 O 3.7X + 3.7 O 2.7
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- 5. Maximum utility occurs when the marginal utility per dollar for both goods is equal. True True O False3. [In class, we noted that the consumer will spend all their money if they have in- creasing preferences. Here, we give a calculus-based condition for the consumer to spend all their money, that doesn't assume more is always better. The con- dition is a stronger version of what is sometimes called "local non-satiation".] Let E X, and let MU, denote the marginal utility for good i € {1,2} at r. (a) Suppose some good i has MU, #0 (it could be positive or negative), and suppose the consumer is not spending all her money at bundle x (that is pr 0 if MU; <0. Argue that the consumer would not optimally choose r. x (b) Suppose MU₁(x) = MU₂(x) = 0, the good is affordable (p ≤ m), and u is concave. Explain why r is optimal.3.5 Marginal Utility and Consumer Choice Participation Question 7: • A consumer derives utility from consuming integer units of Good X and Good Y. See the table below for a total utility level at different consumption levels. What is the marginal utility of the second unit of Good X when the consumption of Good Y is at 3? Total Utility 1 Good X 2 Good X 3 Good X 1 Good Y 1 8. 2 Good Y 8 10 3 Good Y 10 11 A. 10 В. 5 С. 3 D. 2
- Amadea spends all her income on pizza,chocolate milk, and music streams. The price of pizza is $4 per slice and price ofchocolate milk $2 per bottle. At Amadea's current consumption level, her marginalutility for pizza is 50 units per slice and for music 100 units per stream. Assuming thatAmadea is a utility maximizer, how much is (a)her current marginal utility for a bottleof chocolate milk, and (b) the price of streams she buys. Show your work. [Hint: Ch 6:Utility-maximizing formula)Suppose that the following Cobb-Douglas utility function is given U(X,Y) = X³y/2, Which of the following is correct? O Law of diminishing Marginal Utility holds for good Y but not for good X while Law of Diminishing Marginal Rate of Substitution holds. Law of diminishing Marginal Utility holds for good X but not for good Y while Law of Diminishing Marginal Rate of Substitution holds. Law of diminishing Marginal Utility holds for good Y but not for good X while Law of Diminishing Marginal Rate of Substitution fails to hold. Law of diminishing Marginal Utility holds for both goods and Law of Diminishing Marginal Rate of Substitution holds as well4. What kind of preferences are represented by a utility function of the form u(r1, r2) = VI1 + x2? WWhat about the utility function v(r1,r2) = 13.r, + 13.r2? %3D %3D
- Question 3 Gabriel the consumer, has preferences over goods x and y that are perfect substitutes, where utility is u(x,y) = x+y. He has an income of $152. The price of y is $12. If the price of x falls from $8 to $2, then Gabriel's, optimal choice for good x should rise by units. O 51 O53 55 O 57 --Question 21 Units of Product Marginal Utility, A (Price = $1) Marginal Utility, B (Price = $1) First Second Third Fourth Fifth Sixth Seventh 16 utils. O 54 utils. Ⓒ70 utils. 12 Ⓒ20 utils. 10 8 6 4 2 0 16 14 12 10 8 4 Refer to the data for a consumer whose income = $4. In equilibrium, the introduction of new product C has increased this consumer's total utility by Marginal Utility, New Product, C (Price = $1) 20 18 16 14 12 10 8Refer to the accompanying table. The marginal utility of the 3rd dinner is Total Marginal Utility Utility 100 Number of Dinners. Out Per Week 1 2 3 4 Multiple Choice O о O 155. 55. 120. 65. 220 250 65
- Suppose that you have utility function U(x, y) = x2y2, What happens to the share of income spent on each good (, ) when the 1/2 P.X P,y price of x increases? O a. Share spent on x increases O b. Share spent on y increases O c. Both shares stay the same O d. Both shares decrease O e. Not enough information ge Next pageAssume that Robyn wants to buy socks and once she finds out that the price per pair is $5. she decides to buy 4 pairs of socks. Which of the following is true? O a) The marginal benefit (or marginal utility) of the 5th pair is higher than the marginal cost of the Sth pair O b) The marginal benefit (or marginal utility) of the 4th pair must be equal to $20 O O The marginal benefit (or marginal utility) of the Sth pair must be lower than $5 O d) The marginal benefit (or marginal utility) of the first pair must be lower than 55QUESTION 44 What is being described here? "The excess of utility from the consumption of one more unit of a good, over the price paid". O a. Marginal consumer surplus O b. The slope of the indifference curve O c. Marginal utility O d. Total utility