Homework Answers
1) For utility to be increasing in C, U'(c) > 0
=> K1 - K2c > 0 => c < (K1/K2)
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Consider the utility function: with Ki> 0, K2 > 0. (a) For what values of c is the utility functi...
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...
Suppose, as usual, Elmos utility function over gambles satisfies the expected utility property. Consider two gambles...
Suppose, as usual, Elmos utility function over gambles satisfies the expected utility property. Consider two gambles g and h such that E[g] > E[h]. (a) Suppose Elmo is risk-averse. Will Elmo necessarily prefer g to h? Explain. (b) What if Elmo is risk-neutral? Explain. (c) What if Elmo is risk-loving? Explain.
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...
Question 8: Consider a decision-maker with utility function u(x) = x^0.8 , where x>0 denotes the...
Question 8: Consider a decision-maker with utility function u(x) = x^0.8 , where x>0 denotes the decision-maker’s wealth. a. Determine the decision-maker’s attitude towards risk. In other words, is this decision-maker risk-neutral, risk-averse or risk-loving? Provide a justification of your answer. Solution: We have ?''(x) = -0.16x^-1.2 <0 . Hence, the decision-maker is risk-averse. Please explain solution. How did he get the answer?
If so, ind it. I no, explain. 7. Suppose, as usual, Elmos utility function over gambles...
If so, ind it. I no, explain. 7. Suppose, as usual, Elmos utility function over gambles satisfies the expected utility property. Consider two gambles g and h such that E[g]> E[h]. (a) Suppose Elmo is risk-averse. Will Elmo necessarily prefer g to h? Explain. (b) What if Elmo is risk-neutral? Explain. (c) What if Elmo is risk-loving? Explain. QA
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...
2. Consider two lotteries, A and B. With lottery A, there is a 0.90 chance that...
2. Consider two lotteries, A and B. With lottery A, there is a 0.90 chance that you receive a payoff of S0 and a 0.10 chance that you receive a payoff of $400. With lottery B, there is a 0.50 chance that you receive a payoff of S30 and a 0.50 chance that you receive a payoff of $50, a) Verify that these two lotteries have the same expected value but that lottery A has a bigger variance than lottery...
5. A consumer who lives for two periods has a standard Cobb-Douglas utility func- tion: u(C1,C2)...
5. A consumer who lives for two periods has a standard Cobb-Douglas utility func- tion: u(C1,C2) = ccm where ct = consumption in period t and a + b = 1. Her income in period one is 11 = 500 and 12 = 400, and she can lend or borrow at interest rate r = 0.2. (a) Find the optimal consumption demand. (b) What values of a, if any, makes the consumer a borrower? Interpret this result. (c) Suppose now...
4. Suppose Kate has a utility of income function given in the following table Utilit 0...
4. Suppose Kate has a utility of income function given in the following table Utilit 0 Income 0 100 200 300 400 500 600 700 800 900 1000 12 35 48 58 72 76 78 (a) Kate has a choice between $200 with certainty and receiving $100 with probability 0.5 and receiving $300 with probability 0.5. Which will Kate choose? (b) Kate has a choice between $800 with certainty and receiving $600 with probability 0.5 and receiving $1000 with probability...
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...
Suppose, as usual, Elmos utility function over gambles satisfies the expected utility property. Consider two gambles g and h such that E[g] > E[h]. (a) Suppose Elmo is risk-averse. Will Elmo necessarily prefer g to h? Explain. (b) What if Elmo is risk-neutral? Explain. (c) What if Elmo is risk-loving? Explain.
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...
If so, ind it. I no, explain. 7. Suppose, as usual, Elmos utility function over gambles satisfies the expected utility property. Consider two gambles g and h such that E[g]> E[h]. (a) Suppose Elmo is risk-averse. Will Elmo necessarily prefer g to h? Explain. (b) What if Elmo is risk-neutral? Explain. (c) What if Elmo is risk-loving? Explain. QA
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...
2. Consider two lotteries, A and B. With lottery A, there is a 0.90 chance that you receive a payoff of S0 and a 0.10 chance that you receive a payoff of $400. With lottery B, there is a 0.50 chance that you receive a payoff of S30 and a 0.50 chance that you receive a payoff of $50, a) Verify that these two lotteries have the same expected value but that lottery A has a bigger variance than lottery...
5. A consumer who lives for two periods has a standard Cobb-Douglas utility func- tion: u(C1,C2) = ccm where ct = consumption in period t and a + b = 1. Her income in period one is 11 = 500 and 12 = 400, and she can lend or borrow at interest rate r = 0.2. (a) Find the optimal consumption demand. (b) What values of a, if any, makes the consumer a borrower? Interpret this result. (c) Suppose now...
4. Suppose Kate has a utility of income function given in the following table Utilit 0 Income 0 100 200 300 400 500 600 700 800 900 1000 12 35 48 58 72 76 78 (a) Kate has a choice between $200 with certainty and receiving $100 with probability 0.5 and receiving $300 with probability 0.5. Which will Kate choose? (b) Kate has a choice between $800 with certainty and receiving $600 with probability 0.5 and receiving $1000 with probability...
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