Every time, select that investment that provides higher Expected utility
Consider two investments X and Y, where X pays $0 and $10 with equal probability and...
a) (3)) Consider two investments X and Y, where X pays $0 and $10 with equal probability and Y pays 0 with probability 0.75 and $20 with probability 0.25. What investment would an investor choose if her utility function is (0) (ii) (ii) u(x) = x2 u(x) = u(x) = 1-e * = X
Consider two investments X and Y, where X pays $0 and $10 with equal probability and Y pays 0 with probability 0.75 and $20 with probability 0.25. What investment would an investor choose if her utility function is ux=x2 ux=x ux=1-e-x10 Consider an insurance market with insurance firms being competitive and risk neutral (Zero expected profits in equilibrium) and a risk averse customer with a von-Neumann Morgenstern utility function ux=x1/3. The customer is born with a wealth of $150. There...
1. Consider two random variables X and Y with joint density function f(x, y)-(12xy(1-y) 0<x<1,0<p<1 otherwise 0 Find the probability density function for UXY2. (Choose a suitable dummy transformation V) 2. Suppose X and Y are two continuous random variables with joint density 0<x<I, 0 < y < 1 otherwise (a) Find the joint density of U X2 and V XY. Be sure to determine and sketch the support of (U.V). (b) Find the marginal density of U. (c) Find...
Consider a consumer whose utility function is given by U(x, y) = x^1/3 y^2/3, where x and y represent quantities of consumption of two consumer goods. (a) If the consumer’s income is $100 and the prices of x and y are both $1, how should the consumer maximize her utility? What is her maximum level of utility? (b) If the price of y rose to $2, what would be the resulting income and substitution effects? Illustrate your answer.
4. The random variables X and Y have joint probability density function fx.y(r, y) given by: else (a) Find c (b) Find fx (r) and fr (u), the marginal probability density functions of X and Y, respectively (c) Find fxjy (rly), the conditional probability density function of X given Y. For your limits (which you should not forget!), put y between constant bounds and then give the limits for r in terms of y. (d) Are X and Y independent?...
Candy is choosing between Prospect X = ($0, 0.25; $10, 0.25; $20, 0.25; $30, 0.25) Prospect Y = ($10, 0.50; $20, 0.50). Her utility of wealth function is given by = x cubed (3/x) If Candy had to choose between Prospect X and Prospect Y, which would she choose? Prospect X Prospect Y She’d be indifferent between X and Y Cannot be determined
4. The random variables X and Y have joint probability density function fx,y(x, ) given by: fx,y(x, y) 0, else (a) Find c. (b) Find fx(x) and fy (), the marginal probability density functions of X and Y, respectively (c) Find fxjy (xly), the conditional probability density function of X given Y. For your limits (which you should not forget!), put y between constant bounds and then give the limits for in terms of y. (d) Are X and Y...
assume an investor with the following utility function : U= E(r) - 0.60 (s2) to maximize her expected utility, which one of the following investment alternatives would she choose? A. a portfolio that pays 10% with a 60% probablility or 5% with 40% probability B. A portfolio that pays 12% with 40% probability or 5% with 60% probability C. A portfolio that pays 10% with 40% probability or 5% with a 60% probability D. A portfolio that pays 12% with...
Suppose the function u(x) = x0.5 , where x is
consumption, represents your preference over gambles using an
expected utility function.
You have a probability 0.1 of getting consumption xB (bad state)
and a probability 0.9 of getting xG (good state).
An insurance company allows you to choose an insurance contract
(b, p), where b is the insurance benefit the company pays you if
the bad state occurs and p is the insurance premium you pay the
company regardless of...
Calculate the
i.) conditional probability density function of Y given
X=10,
ii.) conditional mean and variance of Y given X =
10
3 6 0 10 20 0.05 0.41 0.08 0.1 0.11 0.25
3 6 0 10 20 0.05 0.41 0.08 0.1 0.11 0.25