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

###### Question details

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?

(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) -
. (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) = −2
+ 𝑦^{2}, (𝑀𝑈_{x} = −
, 𝑀𝑈y = 2𝑦)

(b) 𝑈(𝑥,𝑦) = −𝑥^{2} −𝑦^{2}, (𝑀𝑈_{𝑥} = −2𝑥,
𝑀𝑈𝑦 = −2𝑦)

(c) 𝑈(𝑥,𝑦) = 𝑙𝑛(𝑥) + 2𝑙𝑛(𝑦), (𝑀𝑈_{𝑥} = 1/x, 𝑀𝑈𝑦 = 2/y )

(d) 𝑈(𝑥,𝑦) = 2𝑙𝑛(𝑦) − 𝑙𝑛(𝑥), (𝑀𝑈_{𝑥} = - 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)=
+
, (MU_{B} =
, MU_{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.