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Question: please explain and show any work 1 consider the following...

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Please explain and show any work

1. Consider the following indifference curves for Adam, Ben, Cara, and Doug. Which of the following statements is FALSE?

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(a) Adam likes Y and is neutral towards X. 

(b) Ben always likes X and experiences a diminishing marginal utility. He likes a little bit of Y, but dislikes a lot of Y. When Y is a “good” it exhibits diminishing marginal utility, and when Y is a “bad” it exhibits increasing marginal disutility (i.e. each additional unit is worse than the last). 

(c) Cara likes Y and dislikes X. Her marginal utility of X is constant while her marginal utility of Y is increasing. 

(d) Doug dislikes both X and Y and experiences decreasing marginal disutility for each (i.e. each additional unit is not as bad as the last). 

(e) None of the above statements are false.

2. Rachel has preferences that can be described by the utility function 𝑈(𝑥,𝑦) = 2𝑙𝑛(𝑥) - large rac{1}{2}y^{2} . (𝑀𝑈𝑥 = 2/x, 𝑀𝑈𝑦= −𝑦). Rachel likes X and likes it ____ the more she consumes. Rachel dislikes Y and dislikes it _____the more she consumes. Her indifference curves slope _____at _____rate. (a) less and less; more and more; upward; an increasing
(b) more and more; less and less; upward; an increasing
(c) less and less; more and more; downward; an increasing
(d) more and more; less and less; upward; a decreasing

(e) less and less; more and more; upward; a decreasing

3. For which of the following utility functions will the corresponding indifference curves slope downward at an increasing rate? 

(a) 𝑈(𝑥,𝑦) = −2large sqrt{x} + 𝑦2, (𝑀𝑈x = − large rac{1}{sqrt{x}} , 𝑀𝑈y = 2𝑦)

(b) 𝑈(𝑥,𝑦) = −𝑥2 −𝑦2, (𝑀𝑈𝑥 = −2𝑥, 𝑀𝑈𝑦 = −2𝑦)
(c) 𝑈(𝑥,𝑦) = 𝑙𝑛(𝑥) + 2𝑙𝑛(𝑦), (𝑀𝑈𝑥 = 1/x, 𝑀𝑈𝑦 = 2/y ) 

(d) 𝑈(𝑥,𝑦) = 2𝑙𝑛(𝑦) − 𝑙𝑛(𝑥), (𝑀𝑈𝑥 = - 1/x , 𝑀𝑈𝑦 = 2/y )

(e) None of the above functions. 


4. An individual’s preferences over books (B) and snacks (S) are represented by the utility function, U(B,S)= large {sqrt{B} + VS , (MUB = large rac{1}{2sqrt{B}} , MUS = large rac{1}{2sqrt{S}} ). According to the MRS, what’s the maximum number of books the individual would be willing to give up to obtain one more snack, if the individual currently has 16 snacks and 4 books?
(a) 4
(b) ¼
(c) 2
(d) ½
(e) None of the above statements are true.

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