Answer each part of this question for the utility function given. Justify your answers in words

and using the appropriate derivatives.

a$.(,)=2$

$2$; Is the assumption that more is better satisfied for each good? $(6$ points$)$

b$.(,)=0\mathrm{.}5+2$; Does the marginal utility of X diminish, remain constant, or increase

as the consumer buys more X$,$ holding Y constant? $(6$ points$)$

c$.(,)=4/34/3$; Does the MRS of X for Y diminish, remain constant, or increase as the

consumer substitutes X for Y to the right along an indifference curve? $(7$ points$)$

d$.(,)=+1/2$; Are the associated indifference curves downward sloping and convex

to the origin $($decreasing at a decreasing rate$)?(7$ points$)$