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? 

Are the above statements, c) d) and e) – TRUE, FALSE or UNCERTAIN? Please provide a brief explanation.

For parts c),d) and e) of question 1 assume that there are only three assets in theeconomy; A, B, and C. The returns and standard deviations for the three assets aregiven by:TA =5%, TB = 10%, TC = 12%CA=0%, OB = 10%, oc = 20%The correlation coefficient between assets B and C is:PB,C = 0.7We ask whether these three assets are Mean-Variance efficient. If you claim an assetis efficient prove it explicitly and if it is inefficient show a portfolio that dominatesit. In case you argue that it cannot be determined explain why(c) Asset A Mean-Variance efficient. (10 marks)(d) Asset B Mean-Variance efficient. (10 marks)(e) Asset C Mean-Variance efficient. (10 marks)