Suppose the function u(x) = 2x represents your taste over gambles using an expected utility function....

Suppose the function u(x) = 2x represents your taste over gambles using an expected utility function. Consider a gamble that will result in a lifetime consumption of x0 with probability p, and x1 with probability 1 – p, where x1 > x0.

(a) Are you risk averse? Explain.

(b) Write down the expected utility function.

(c) Derive your certainty equivalent of the gamble. Interpret its meaning.

(d) What is the expected value of the gamble?

(e) What is the risk premium of the gamble?

Expert Solution

Rahul Sunny answered 1 year ago

Your utility function over x and y is U ( x , y ) = l...

Your utility function over x and y is U ( x , y ) = l n ( x ) + 0.25 y. Your income is $20. You don’t know the prices of x or y so leave them as variables (p x and p y). a) (8 points) Find x*, your demand function for x. Find y*, your demand function for y. b) (10 points) Find the cross-price elasticity of demand for x (E x ∗ , p y:...

Suppose a consumer has a utility function u(x, y) = 2x + 3y. The consumer has...

Suppose a consumer has a utility function u(x, y) = 2x + 3y. The consumer has an income $40 and the price of x is $1 and the price of y is $2. Which bundle will the consumer choose to consume? Determine the demand functions for x and for y. Repeat the exercise if, instead, the consumer’s utility function is u(x, y) = min{x, 2y}.

Given the function u(x) = x0.5 , where x is consumption and represents your preference over...

Given the function u(x) = x0.5 , where x is consumption and represents your preference over gambles using an expected utility function. There is a probability of 0.1 in getting consumption xB (bad state) and a probability 0.9 of getting xG (good state). An insurance company allows people to choose an insurance contract (b, p), where b is the insurance benefit the company pays if the bad state occurs, and p is the insurance premium paid to the company regardless...

Suppose a consumer's utility function is given by U ( X , Y ) = X...

Suppose a consumer's utility function is given by U ( X , Y ) = X 1 2 Y 1 2. The price of X is PX=8 and the price of Y is PY=5. The consumer has M=80 to spend. You may find that it helps to draw a graph to organize the information in this question. You may draw in the blank area on the front page of the assignment, but this graph will not be graded. a) (2...

What are the similarities and differences between the utility function (i.e., u(x)) in the expected utility...

What are the similarities and differences between the utility function (i.e., u(x)) in the expected utility theory and the value function (i.e., v(x)) in the reference-dependent theory (i.e., the prospect theory)?

Suppose that the utility function of a consumer is U(x,y) = x ¼y ¾, where x...

Suppose that the utility function of a consumer is U(x,y) = x ¼y ¾, where x and y are the quantities of the good X and good Y consumed, respectively. The consumer's income is 400. (a) What is the demanded bundle when the price of good X is 10 and the price of good Y is 10? (b) Redo part (a) when the price of good X is doubled? (c) Redo part (a) when the price of good Y is...

Jim’s utility function is U(x, y) = xy. Jerry’s utility function is U(x, y) = 1,000xy...

Jim’s utility function is U(x, y) = xy. Jerry’s utility function is U(x, y) = 1,000xy + 2,000. Tammy’s utility function is U(x, y) = xy(1 - xy). Oral’s utility function is -1/(10 + xy. Billy’s utility function is U(x, y) = x/y. Pat’s utility function is U(x, y) = -xy. a. No two of these people have the same preferences. b. They all have the same preferences except for Billy. c. Jim, Jerry, and Pat all have the same...

Your utility function is U = 10 X 0.1Y 0.7 and your marginal utility functions are...

Your utility function is U = 10 X 0.1Y 0.7 and your marginal utility functions are MUx=X^−0.9 Y^ 0.7 MUy=7X^ 0.1 Y^−0.3 Your budget is M and the prices of the two goods are pX and pY . a) Write down the two conditions for utility maximization subject to a budget constraint. b) Derive the demand functions for X and Y . c) Based on your demand functions explain whether: - Y is a normal good or an inferior good...

Suppose your utility function is U(x,y)=2ln⁡(x)+4y. a) Solve for the individual demand for good x and...

Suppose your utility function is U(x,y)=2ln⁡(x)+4y. a) Solve for the individual demand for good x and the individual demand for good y. b) Given Px = 1, Py = 2, and M = 5, find the income elasticity of demand for good x -- is good x normal or inferior (or neither)? Also find the income elasticity of demand for good y -- is good y normal or inferior (or neither)? c) Given Px = 1, Py = 2, and...

Suppose your utility function is U(x,y) = 2ln(x)+4y a) Solve for the individual demand for good...

Suppose your utility function is U(x,y) = 2ln(x)+4y a) Solve for the individual demand for good x and the individual demand for good y. b) Given Px = 1, Py = 2, and M = 5, find the income elasticity of demand for good x -- is good x normal or inferior (or neither)? Also find the income elasticity of demand for good y -- is good y normal or inferior (or neither)? c) Given Px = 1, Py =...

Question