Homework Answers
A) risk lover
B risk averse
C risk Neutral
D risk lover
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Do the following utility functions describe risk averse, risk loving or risk neutral individuals? a. utility...
Problem 1. Do the following utility functions represent risk-averse, risk-neutral or risk-loving preferences? Motivate your answers....
Problem 1. Do the following utility functions represent risk-averse, risk-neutral or risk-loving preferences? Motivate your answers. In each question, w is the wealth. (a) u(w)10w3 c) u(w)-e4 (d) u(w)-1- e
2. (a) Explain the terms risk averse, risk loving and risk neutral with the aid of...
2. (a) Explain the terms risk averse, risk loving and risk neutral with the aid of diagrams. Jane's utility (U) depends upon her income( Y) according to the following table U(Y) 50 7 100 9.5 150 200一一 14 250 300 350 12 16.5 17 19 She has received a prize with an uncertain value. In particular, with probability 0.25 she wins $300 and with probability 0.75 she wins $100. (b) What is the expected payoff from this prize? What is...
An individual with a constant marginal utility of income will be: o risk neutral risk averse....
An individual with a constant marginal utility of income will be: o risk neutral risk averse. risk loving insufficient information for a decision
6. Consider an individual whose utility function over money is u(w)= 1+2w2. (a) Is the individual...
6. Consider an individual whose utility function over money is u(w)= 1+2w2. (a) Is the individual risk-averse, risk-neutral, or risk-loving? Does it depend on w? (b) Suppose the individual has initial wealth ¥W and faces the possible loss of Y". The probability that the loss will occur is . Suppose insurance is available at price p, where p is not necessarily the fair price. Find the optimal amount of insurance the individual should buy. You may assume that the solution...
Question 1 Consider the following three utility functions defined over quantities of money. These functions are...
Question 1 Consider the following three utility functions defined over quantities of money. These functions are risk-neutral, risk-loving, and risk-averse. Match each utility function to its risk attitude u = x^2 [Choose) [Choose ] risk-averse risk loving risk-neutral u = log(x) [Choose ] u = x + 5 Consider two firms, a farm and a railroad, both of whom maximize expected profits. The railroad emits sparks from its engines which sometimes ignite fires on the farm. There is a 1/10...
6. A decision maker has a vNM utility function over money of u(x) = x2. This...
6. A decision maker has a vNM utility function over money of u(x) = x2. This decision maker is (a) risk-averse. (b) risk-neutral. (c) risk-loving. (d) none of the above. 7. Consider two lotteries: • Lottery 1: The gamble (0.1, 0.6, 0.3) over the final wealth levels ($1, $2, $3). (The expected value of this lottery equals $2.2) • Lottery 2: Get $2.2 for sure. a) Any risk-averse individual will choose the first lottery. b) Any risk-averse individual will choose...
Consider the utility function: with Ki> 0, K2 > 0. (a) For what values of c is the utility functi...
Consider the utility function: with Ki> 0, K2 > 0. (a) For what values of c is the utility function increasing? (b) For what range of values does it make sense to suppose that this is the agent's utility function? treat this as the agent's utility function? (for the range for which utility is increasing in consumption)? (c) Suppose that Ki = 5,K2 = 2, For what range of values does it make sense to (d) Is an agent who...
Describe analytically and graphically how a risk-averse decision-maker differs from a risk-neutral decision-maker.
Describe analytically and graphically how a risk-averse decision-maker differs from a risk-neutral decision-maker.
For each of the utility functions below, compute the Arrow-Pratt coefficients of risk-aversion. Say whether the utility...
For each of the utility functions below, compute the Arrow-Pratt coefficients of risk-aversion. Say whether the utility functions have constant absolute risk aversion, increasing absolute risk aversion, or decreasing absolute risk aversion. (a) u(w) = a + Bw where B > 0. (b) u(w) = w2. (c) u(w) = w1/2 (d) u(w) = wl-/(1-0) where o € (0,1). (e) u(w) =1-e-aw where a > 0.
1. Suppose that I give you the following utility function There are two potential outcomes. With ...
1. Suppose that I give you the following utility function There are two potential outcomes. With probability 1/2 there is good news and Yo-9. If there is bad news then YB = 3. a) What is the expected value of Y? b) What is the expected utility of the consumer with the utility function above? c) Is expected utility greater than, equal to or less than the expected value? Does this mean that the consumer is risk averse, risk neutral...
Problem 1. Do the following utility functions represent risk-averse, risk-neutral or risk-loving preferences? Motivate your answers. In each question, w is the wealth. (a) u(w)10w3 c) u(w)-e4 (d) u(w)-1- e
2. (a) Explain the terms risk averse, risk loving and risk neutral with the aid of diagrams. Jane's utility (U) depends upon her income( Y) according to the following table U(Y) 50 7 100 9.5 150 200一一 14 250 300 350 12 16.5 17 19 She has received a prize with an uncertain value. In particular, with probability 0.25 she wins $300 and with probability 0.75 she wins $100. (b) What is the expected payoff from this prize? What is...
An individual with a constant marginal utility of income will be: o risk neutral risk averse. risk loving insufficient information for a decision
6. Consider an individual whose utility function over money is u(w)= 1+2w2. (a) Is the individual risk-averse, risk-neutral, or risk-loving? Does it depend on w? (b) Suppose the individual has initial wealth ¥W and faces the possible loss of Y". The probability that the loss will occur is . Suppose insurance is available at price p, where p is not necessarily the fair price. Find the optimal amount of insurance the individual should buy. You may assume that the solution...
Question 1 Consider the following three utility functions defined over quantities of money. These functions are risk-neutral, risk-loving, and risk-averse. Match each utility function to its risk attitude u = x^2 [Choose) [Choose ] risk-averse risk loving risk-neutral u = log(x) [Choose ] u = x + 5 Consider two firms, a farm and a railroad, both of whom maximize expected profits. The railroad emits sparks from its engines which sometimes ignite fires on the farm. There is a 1/10...
Consider the utility function: with Ki> 0, K2 > 0. (a) For what values of c is the utility function increasing? (b) For what range of values does it make sense to suppose that this is the agent's utility function? treat this as the agent's utility function? (for the range for which utility is increasing in consumption)? (c) Suppose that Ki = 5,K2 = 2, For what range of values does it make sense to (d) Is an agent who...
For each of the utility functions below, compute the Arrow-Pratt coefficients of risk-aversion. Say whether the utility functions have constant absolute risk aversion, increasing absolute risk aversion, or decreasing absolute risk aversion. (a) u(w) = a + Bw where B > 0. (b) u(w) = w2. (c) u(w) = w1/2 (d) u(w) = wl-/(1-0) where o € (0,1). (e) u(w) =1-e-aw where a > 0.
1. Suppose that I give you the following utility function There are two potential outcomes. With probability 1/2 there is good news and Yo-9. If there is bad news then YB = 3. a) What is the expected value of Y? b) What is the expected utility of the consumer with the utility function above? c) Is expected utility greater than, equal to or less than the expected value? Does this mean that the consumer is risk averse, risk neutral...
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