There is a mass 1 of identical entrepreneurs with the variable-investment technology described in Section 3.4. The representative entrepreneur has wealth A, is risk neutral, and is protected by limited liability. Denote the average investment by I and the indi- vidual investment i (in equilibrium i = I by symme- try but we need to distinguish the two in a ﬁrst step in order to compute the competitive equilibrium). A project produces Ri units of goods when successful and 0 when it fails. The probability of success is pH in the case of good behavior (the entrepreneur receives no private beneﬁt) and pL = pH − ∆p in the case of misbehavior (the entrepreneur then receives private beneﬁt Bi). Assume that it is optimal to induce the entrepreneur to behave. The market price of output is P = P(Q), with P' 0, where Q is aggregate production (with P(Q) tend- R ≡ RS − RF denote the increase in income from the low to the high level. Show that the debt contract is optimal, but unlike in the variable-investment case it may not be uniquely optimal.

There is a mass 1 of identical entrepreneurs with the variable-investment technology described in Section 3.4. The representative entrepreneur has wealth A, is risk neutral, and is protected by limited liability. Denote the average investment by I and the indi- vidual investment i (in equilibrium i = I by symme- try but we need to distinguish the two in a ﬁrst step in order to compute the competitive equilibrium). A project produces Ri units of goods when successful and 0 when it fails. The probability of success is pH in the case of good behavior (the entrepreneur receives no private beneﬁt) and pL = pH − ∆p in the case of misbehavior (the entrepreneur then receives private beneﬁt Bi). Assume that it is optimal to induce the entrepreneur to behave. The market price of output is P = P(Q), with P' 0, where Q is aggregate production (with P(Q) tend- R ≡ RS − RF denote the increase in income from the low to the high level. Show that the debt contract is optimal, but unlike in the variable-investment case it may not be uniquely optimal.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.8P

See similar textbooks

Similar questions

Question 2An investor is to purchase one of three types of real estate, as illustrated inFigure below. The investor must decide among an apartment building, anoffice building, and a warehouse. The future states of nature that willdetermine how much profit the investor will make are good economicconditions and poor economic conditions. The profits that will result fromeach decision in the event of each state of nature are shown in Table below: Assume that it is now possible to estimate a probability of 0.60 that goodeconomic conditions will exist and a probability of .40 that poor economicconditions will exist. a) Determine the best decision by using expected opportunity loss. b) Develop a decision tree, with expected values at the probability nodes. c) Compute the expected value of perfect information.
What are pure specific factors model and mixed pecific factors model? How does the two differ?
What are the major assumptions underlying the Markov Chain? What are the major application problems of Markov analysis in business decisions?
You and a coworker are assigned a team project on which your likelihood or a promotion will be decidedon. It is now the night before the project is due and neither has yet to start it. You both want toreceive a promotion next year, but you both also want to go to your company’s holiday party that night.Each of you wants to maximize his or her own happiness (likelihood of a promotion and mingling withyour colleagues “on the company’s dime”). If you both work, you deliver an outstanding presentation.If you both go to the party, your presentation is mediocre. If one parties and the other works, yourpresentation is above average. Partying increases happiness by 25 units. Working on the project addszero units to happiness. Happiness is also affected by your chance of a promotion, which is depends on howgood your project is. An outstanding presentation gives 40 units of happiness to each of you; an aboveaverage presentation gives 30 units of happiness; a mediocre presentation gives 10 units…
QUESTION Sahar is analyzing the probability to open her own beauty salon. If she chooses to operate her own salon she would have to pay Rs. 70,000 p.m as rent and staff that would cost her Rs. 30,000 p.m and is expected to earn Rs. 150,000 p.m. While if she continues working as the head makeup artist in one of renowned salons of Karachi she would earn 120,000. Analyze the information above and find explicit and implicit cost?
Question 3 Consider a medieval Italian merchant who is a risk averse expected utility maximiser. Their wealth will be equal to y if their ship returns safely from Asia loaded with the finest silk. If the ship sinks, their income will 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 cer- tainty equivalent income in a 2-dimensional state-contingent consumption space. (ii) Use the diagram to illustrate and explain how the merchant would benefit from buying insurance in a competitive insurance market. At which point a risk-neutral insurance firm would maximise their profits by offering the merchant full insurance?
Prove that APC + APS = 1 how please explain it???
2 Scenario Your client, InsureCorp, is an insurance company considering launching an 'income insur- ance' product in the nation of Motherland. Income insurance is a product that fully insures a household against changes in income caused by a major injury or illness. At present, no businesses are selling income insurance products in Motherland. Initial market research suggests that there are 15,000 households in Motherland interested in purchasing income insurance. Your client expects that the fixed cost of launching the income insurance product will be $25,000,000 per year, and that each policy issued to a customer will cost the company an additional $2,000 in sales commissions. 2.1 Your task Your client wants you to analyse the potential market for income insurance and report on the following: What is the maximum price the company can charge a household for an income insurance policy? What is the expected profit (or loss) for the company if it becomes a monopoly provider of income…
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.
9) A risk-neutral individual with current wealth w has already decided investing all his wealth in a project that has two possible net wealth outcomes wn and we (with probabilities pr and pe, respectively) where wr > w > we > 0, PrPe E (0,1), and pr + Pe = 1. Before he invests, he realises that there is a source of information that tells the individual which outcome will be realised with truth, what is the value of this information for the individual? a) pe(@ – w;), b) (Pn – Pe)w, c) Phwn + PeWe – w, d) Pr(w – wn).
The Constant Relative Risk Aversion (CRRA) utility function is a widely used specifica- tion of preferences in economics that captures risk aversion and intertemporal consump- tion smoothing. The CRRA utility function has the desirable property that the degree of risk aversion is constant and independent of the level of consumption. This means that as a household's consumption grows, its willingness to take risks remains the same. The coefficient of relative risk aversion (σ) measures the extent to which households are risk- averse and prefer a smooth consumption path over time. A higher value of σ indicates a greater degree of risk aversion and a stronger preference for consumption smoothing. Consider a two-period endowment economy with a large number of identical house- holds. Each household has the following lifetime utility function: U(j) = C+(j) 1-0 - 1 1-σ +ẞ C++1(j) 1-0 - 1 1-σ where C₁(j) and C++1(j) are consumption in periods t and t + 1 for household j, re- spectively, ẞ is…
4) Consider investors with preferences represented by the utility function U = E(r) – Ao². (a) Draw the indifference curve representing a utility level of 10% for an in- vestor with a risk aversion parameter A = 3 in expected return-standard deviation space. (b) In the same graph, draw the indifference curve representing a utility level of 15% for an investor with a risk aversion parameter A = 3. (c) In the same graph, draw the indifference curve representing a utility level of 10% for an investor with a risk aversion parameter A = 5.