4.Consider the following quadratic utility function, U(W) = 100 + 180W - 3W2 that describes the preferences for a given investor. Which of the following statements is not correct regarding this utility function? a.This utility function is consistent with the investor "preference of more to less" assumption for all levels of wealth First derivative is only positive for W< 30, second derivative is always negative b.This utility function is consistent with the assumption of investor risk aversion for all levels of wealth c.This utility function is consistent with the assumption of investor risk aversion for levels of wealth less than W = 30 d.This utility function is consistent with the investor "preference of more to less" assumption for levels of wealth less than W = 30 e.This utility function implies does not rely on the assumption of security returns being jointly normal

Consider the following statements for an investor regarding a quadratic utility function of the form U= E(r)-0.5*A*(SD)^2 Where, U= Utility; E(r)= expected return on the portfolio; A= coefficient of risk-aversion; (SD)^2= Variance of returns Statement (1) When the value of A=0, it suggests that the investor is risk-neutral Statement (2) When the value of A is negative, it suggests that the investor is risk-averse Statement (3) When the value of A is positive, it suggests that the investor is risk-lover Which of these above statements is (are) CORRECT? • a. Statement (1) only. • b. Statement (1) and statement (2) only. • c. Statement (2) and statement (3) only. • d. Statement (1) and statement (3) only. O e. Statement (1), statement (2) and statement (3).

Question 1Joe’s preferences are described by the following utility functionU (x, y) = xαyβwith α > 0 and β > 0.(a) Let I denote Joe’s income, and px and py denote the prices of good x and y, respectively.Find Joe’s optimal consumption bundle.

Suppose that in addition to the consumer described inExercise 1 we also have an another consumer, Consumer 2, whose pref-erences are given by the utility functionu2(x1, x2) = x1x2where x1 is the amount of good 1 the consumer consumes and x2 theamount of good 2. Let ωℓ2 be Consumer 2’s initial endowment of goodℓ. [This is the utility function you analysed in Homework 1.] Similarlylet u1(x1, x2) = min{x1, x2} be the utility function for Consumer 1 thatyou discussed in the previous exercise and ωℓ1 be Consumer 1’s initialendowment of good ℓ.(1) Repeat the analysis of the previous exercise for Consumer 2,finding the demand functions x12(p1, p2, ω12, ω22) andx22(p1, p2, ω12, ω22)

4. The variable (A) in the utility function represents the:A. investor's return requirement.B. investor's aversion to risk.C. certainty-equivalent rate of the portfolio.D. minimum required utility of the portfolio.E. none of the above.1Downloaded by My H?u Ng?c ([email protected])lOMoARcPSD|13409944

There are two goods in the economy, wine and cheese. The price of wine is p1 dollars per litre of wine. The price of cheese is p2 per kilogram of cheese. The consumer has wealth M dollars to spend on wine and cheese. Let x1 denote the quantity of wine in litres she chooses to buy and let x2 denote the quantity of cheese in kilograms she chooses to buy. Suppose throughout that she can only purchase non-negative quantities of either good. Solve the following utility maximization problems when the preferences of a consumer are characterized by the following utility functions. For each part clearly specify what is the quantity of each good the consumer wishes to purchase given her budget constraint. (a) (10 points) U (x1; x2) = x1 x 4 2 [Hint: MU1 (x1; x2) = x 4 2 and MU2 (x1; x2) = 4x1x 3 2 .] (b) (15 points) U (x1; x2) =  x1 + 2x2 ￾ x 2 2 if x2  1 x1 + 1 if x2 > 1 [Hint: MU1 (x1; x2) = 1 and MU2 (x1; x2) = 2 (1 ￾ x2). First work out the solution for the case in which x 1 > 0 and x 2 > 0. Then show if p2 > 2p1 it is optimal for our consumer to spend her entire wealth on wine.] (c) (5 points) U (x1; x2) = maxfx1; x2g That is, U (x1; x2) =  x1 if x1  x2 x2 if x1 < x2 . Warning: In this case MU1 (x1; x2) and MU2 (x1; x2) do not exist! [Hint: Reason from Örst principles how the individual should allocate her wealth between the two goods if her aim is to maximize a utility function of this form. To do this, I recommend drawing a diagram to graph the budget set for di§erent price ratios. Can you Ögure out which 2 bundle or bundles maximise her utility for each particular budget set? To complete your answer you should now be able to work out for general prices and income levels which bundle or bundles maximize her utility.]