An employer has hired Freddy and the current compensation contract gives Freddy $6,600 with prob. 0.3 and $1,550 with prob. 0.7. Assume Freddy is risk averse, with the utility function u(x) = x0.5. The employer is considering changing the contract so that Freddy is paid a fixed X, where X is equal to the expected value of the current contract In this

An employer has hired Freddy and the current compensation contract gives Freddy $6,600 with prob. 0.3 and $1,550 with prob. 0.7. Assume Freddy is risk averse, with the utility function u(x) = x0.5. The employer is considering changing the contract so that Freddy is paid a fixed X, where X is equal to the expected value of the current contract In this

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider a medieval Italian merchant who is a risk averse expected utility maximiser. Their wealth will beequal to y if their ship returns safely from Asia loaded with the finest silk. If the ship sinks, their incomewill be y − L. The chance of a safe return is 50%.(i) Draw and carefully label the merchant’s endowment point, their expected income, and their certainty equivalent income in a 2-dimensional state-contingent consumption space. Use the diagram to illustrate and explain how the merchant would benefit from buying insurancein a competitive insurance market. At which point a risk-neutral insurance firm would maximisetheir profits by offering the merchant full insurance?
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When the second order derivative of a function is greater than zero than the agent is risk lover. question; Asses the risk attitude of an agent represented by the expected utility function u(x)= 2x2-5. However my course material writes that this agent is risk neutral because it is affine. My question is that whys is this so despite the fact that the second order derivative is '4' which is >0. Kindly explain this to me with complete steps.
Consider the model of competitive insurance. Peter is a risk averse individual with the utility function u(w) = w0.5. His current wealth is $300 and with probability 1/2 he will incur a loss of D = $240, but with probability 1/2 he will incur no loss. Ann has the same utility u(w) = w0.5 and current wealth $300 as Peter, but a different probability of loss: she will incur a loss of D = $240 with probability 0.3, and no loss with probability 0.7. In the separating equilibrium Peter is offered actuarially fair full insurance contract, so his wealth is equal to $180, whether loss happens or not. What amount of insurance (approximately) will Ann be offered an insurance contract with?
Consider an economy with two agents where agents A and B where both have the same risk attitude given by u(x)=ln(x). Suppose in state 1, only agent A has a job that earns $3 and B does not earn anything. In state 2, only B works and earns $2. Solve for the equilibrium in this economy when mutual insurance is feasible. Assume both states are equally likely.
Khalid has a utility function U = W1/2, where W is his wealth in millions of dollarsand U is the utility he obtains from the wealth. In a game show, the host offershim a choice between (A) $4 million for sure, or (B) a gamble that pays $1million with probability 0.6 and $9 million with probability 0.4.i. Graph Khalid’s utility function with the help of above utility function. Ishe risk lover? Explain. ii. Does A or B choice offer Khalid a higher expected prize? Explain yourreasoning with appropriate calculations. iii. Does A or B offer Khalid a higher expected utility? Again, show yourcalculations. iv. Should Jamal pick A or B choice? Why?