A firm faces a worker who may be one of two types, with equal probabilities. The firm's profits from a type i worker are given by π₁ = Cį — Si, i = 1, 2, where e; is the effort supplied by a type i worker and and s; is the payment to a type i worker. The cost function of the more productive worker (type 1) is given by c₁ = e² and the cost function of the less productive worker (type 2) is given by c₂ = ae², where a > 1. The utility function of a worker of type i is given by: u¡ = Sį — Cį. Find the solution to the firm's problem (assuming that effort is observable and contractible).
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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 a worker who works for at most two periods (say, when young and when old) at a particular firm. Each period, the worker can choose between exerting high effort and exerting low effort. The worker's cost of exerting high effort are Cy when young and Co when old. The worker's cost of exerting low effort are zero. The effort of the worker is difficult to observe by the firm. With probability T, the firm observes the worker's effort at the end of a period. With the remaining probability, the firm does not observe the worker's effort. The firm can only fire the worker when it observed that the worker has shirked. In that case, the firm is also allowed to withhold the worker's wage for the period in which the worker was caught shirking. When exerting high effort, the worker's productivity is q, when young and q, when old. When exerting low effort, the worker's productivity is zero. The worker's value of alternative job opportunities is when young and v, when old. For simplicity, the…Prove that APC + APS = 1 how please explain it???
- A particular road is used by N drivers each day. Each driver obtains a benefit v from the journey and incurs a cost c(N) that increases with the number of drivers on the road due to congestion. Suppose that the cost incurred is given by c(N) = a + bN, for some positive numbers a, b. If the agent decides not to use the road, they receive 0. You may assume throughout that the number of drivers N can be any real number (rather than an integer). Each driver uses the road at most once. Suppose that the government charges a toll t (a congestion charge) for each journey. Find the optimum toll. Interpret your answer in terms of the externality that each driver imposes on othersExercise 3.17 (competitive product market interac- tions). 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…QUESTION 16 Suppose workers can be divided into two groups: high and low skill workers. Let y be the number of years of college education of a worker. For workers in Group A (high skill workers) the cost of attaining an educational level y is CÃ(y)=$25y; for workers in Group B (low skill workers) the cost of attaining an educational level y is CB(y)=$65y. Employees will be offered $410 if they have y ≥ y*, where y* is an educational threshold determined by the employer. They will be offered $50 if they have y y* z
- Q-3 Are the following statement true of false ? You need to provide an aurgument for and against it why it is so.You received a significant amount of donation D>0 and would like to use this money to run a charity program. Assume that you want the charity program to run for T periods, and you would like to spread the spending overtime. Let st be the spending for period t. Denote di the funding available from the beginning of time t (do = D). The utility (happiness) you receive by helping others (spending St) can be summarized as B'u(st) t=0 where 3 is the discount factor. (3) Assume T = 3. Let u(s) = ln(s), solve the optimal s; for each period.Suppose a college athlete is deciding on when to turn pro (right out of high school, or after 1/2/3/4 years of college). If they go to college, their potential earnings increase by rate r (which is different for every year spent in college). But they have to postpone their earnings by 1 more year and pay discount rate i. What is the general decision rule for staying in school for one more year vs turning pro?
- Reactors `R’ Us operates a nuclear power plant in Potsdam.In the event of reactor failure, there would be major damages to the North Country. The company can reduce the probability of failure through proper maintenance of the facility. The marginal cost of maintenance is increasing in the amount of maintenance done (and thus decreasing in the probability of an accident). We can write this marginal cost curve as MAC=2-10p (where 0<p<1, and represents the probability of a failure over a 50 year period). The marginal expected damages are an increasing function of the probability of an accident so that MD=2.2+10p. Provide a graph or graphs to illustrate your analysis/answers to the following questions. A. What is the efficient probability of reactor failure? B. If “Reactors ‘R’ Us” thinks that, in the event of reactor failure, they will NOT be found liable for damages, what probability of failure will they choose? C. If “Reactors ‘R’ Us” thinks that, in the…Question 13 Consider a market in which there are two types of workers L and H. Each type of worker has a different level of productivity, but that productivity is unobservable ex ante to potential employers. Before seeking employment at a firm in the market, all workers can (if they choose) get some level of education e. This choice of education e is observable to all, including potential employers. Assume that the market is competitive, so expected profits must be zero in equilibrium. The L-type workers have a productivity of 2 if they work for a firm in the market. They also have an outside option of 2. The utility function of the L-type workers UL - wL- eL, where wl is the wage received and eL is the level of education they obtain. The H type worker has an outside option of 2 and a productivity of 4 if they are employed by a firm in the market. The utility function for a H-type worker is UH=wH - (%)eH, where wH is the wage paid to a H-type and eH is the education they choose to get.…Suppose there are two types of workers. Type 1 workers have a marginal product of labor (MPL) = 1. That is, if a firm hires an extra Type I worker, that worker will produce 1 extra unit of output. Type II workers have a MPL = 2. The firm can sell each extra unit of output for P = $12,000. Firms are unable to identify whether or not a worker is Type I or Type Il unless the worker sends a signal of what type they are. The signal that workers can send is a level of education, e. The firm adopts the following hiring strategy: If e >e* then offer the worker a wage rate equal to $24,000. If e < e* then offer the worker a wage rate equal to $12,000. The cost to Type I workers of getting education level e is $4000*e. The cost to Type II workers of getting education level e is $2000*e. If the firm sets e* = 8, which of the following statements is true? O Type I workers will not get e*, but Type II workers will get e*, which means there is a separating equilibrium. O Neither type of workers will…