Nikki cares about two things: how much leisure time she has (x1) and what mark she gets on tomorrow’s Micro exam (x2).

1. Nikki cares about two things: how much leisure time she has (x1) and what mark she gets on tomorrow’s Micro exam (x2). Her preferences between these goods can be represented by the utility function:

u(x1, x2) = x1 + x2

Nikki has 16 hours of today to distribute between studying and relaxing (she sleeps the other 8). Studying positively affects Nikki’s mark up to a certain point, but if she tries to cram too much studying into one day, she will get tired and do worse on tomorrow’s exam. Where s represents the hours Nikki spends studying, the relationship between her mark and s is as follows:

where a > 0.

(a) Suppose a = 6. At what level of s does continuing to study negatively affect

Nikki’s mark?

(b) Suppose a = 6. Write down Nikki’s constraint: the relationship between x1 and

x2 that holds if Nikki uses all her 16 hours for either leisure or studying.

(c) Suppose a = 6. Find Nikki’s optimal choice of x1 and x2.

(d) For what values of a is Nikki’s optimal choice a boundary solution in which she spends all 16 hours studying? 

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