Consider an individual with the following utility function u(W) = W^(1/4) and u(W) = W^(1/2) Which...
Consider an individual with the following utility function u(W) = W^(1/4) and u(W) = W^(1/2)
Which of the utility functions makes the individual more risk Averse (in relative sense)?
Which of the utility functions makes the individual more Prudent? Why or Why not?
Homework Answers
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Consider an individual with the following utility function u(W)
= W^(1/4) and u(W) = W^(1/2)
Which...
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...
8. An individual with utility function over money u(w) = 8Vw has $C in cash and...
8. An individual with utility function over money u(w) = 8Vw has $C in cash and a lottery ticket that pays $W if it wins and nothing if it loses. The probability of winning is .. Suppose an insurance is available at price $p per unit, where each unit of insurance pays $1 if the ticket does not win and nothing if it wins. (a) Is the individual risk averse, risk neutral, or risk loving? (b) What is the fair...
Ann is risk-averse with a Bernoulli utility function u(w) = 100 + w^1/2 where w is...
Ann is risk-averse with a Bernoulli utility function u(w) = 100 + w^1/2 where w is her wealth in dollars. Ann’s current wealth is one million dollars, including her small boat valued at $180, 000. She estimates that with 10% probability the boat will sink and lose its full value; with 15% probability there will be damages and the boat will lose half its value, and with 25% probability the boat will lose a quarter of its value; otherwise, the...
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...
Consider the utility function, defined for 1 = 0; w1-1-1 u(w) =- 1-) Compute the Arrow-Pratt...
Consider the utility function, defined for 1 = 0; w1-1-1 u(w) =- 1-) Compute the Arrow-Pratt coefficient of relative risk aversion for this func- tion.
16. Based on the Relative Risk Aversion (RR) and CRRA utility function (with y 1) and...
16. Based on the Relative Risk Aversion (RR) and CRRA utility function (with y 1) and the odds result: 1 0 70(,0) = 5 +7 a. What is the coefficient of risk aversion (Y) that makes roy, 0)=1, when y=100 and 0 =0.50? b. What is the coefficient of risk aversion (Y) that makes moy, 0)=1, when y=100 and 6 -0.25? c. Which individual is more risk averse based on the coefficient of risk aversion? d. What is the coefficient...
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...
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...
intermediate micro 4. Steve's utility function over leisure and consumption is given by NLY) - min...
intermediate micro
4. Steve's utility function over leisure and consumption is given by NLY) - min (31.7. Wage rate is w and the price of the composite consumption good is p=1. (a) Suppose w = 5. Find the optimal leisure consumption combination. What is the amount of hours worked? (b) Suppose the overtime law is passed so that every worker needs to be paid 1.5 times their current wage for hours worked beyond the first 8 hours, Will this law...
Consider the following utility function introduced in the lecture. U = E(r) − 1/2 Aσ2 Suppose...
Consider the following utility function introduced in the lecture. U = E(r) − 1/2 Aσ2 Suppose there are 3 types of financial securities one can choose to invest in. Expected return and standard deviation of each of these securities are as follows. E(r1) = .13; σ1 = .3 E(r2) = .15; σ2 = .5 E(r3) = .20; σ3 = .2 (a) Which of these three securities would a risk averse investor with A = 4 choose to invest, given that...
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...
8. An individual with utility function over money u(w) = 8Vw has $C in cash and a lottery ticket that pays $W if it wins and nothing if it loses. The probability of winning is .. Suppose an insurance is available at price $p per unit, where each unit of insurance pays $1 if the ticket does not win and nothing if it wins. (a) Is the individual risk averse, risk neutral, or risk loving? (b) What is the fair...
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...
Consider the utility function, defined for 1 = 0; w1-1-1 u(w) =- 1-) Compute the Arrow-Pratt coefficient of relative risk aversion for this func- tion.
16. Based on the Relative Risk Aversion (RR) and CRRA utility function (with y 1) and the odds result: 1 0 70(,0) = 5 +7 a. What is the coefficient of risk aversion (Y) that makes roy, 0)=1, when y=100 and 0 =0.50? b. What is the coefficient of risk aversion (Y) that makes moy, 0)=1, when y=100 and 6 -0.25? c. Which individual is more risk averse based on the coefficient of risk aversion? d. What is the coefficient...
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...
intermediate micro
4. Steve's utility function over leisure and consumption is given by NLY) - min (31.7. Wage rate is w and the price of the composite consumption good is p=1. (a) Suppose w = 5. Find the optimal leisure consumption combination. What is the amount of hours worked? (b) Suppose the overtime law is passed so that every worker needs to be paid 1.5 times their current wage for hours worked beyond the first 8 hours, Will this law...
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