Answer all plzz

Vinton Auto Insurance is deciding how much money to keep in its checking accounts to cover insurance claims. In the past, the company held some of the premiums it received in interest-bearing checking accounts and put the rest into investments that are not quite as liquid, but tend to generate a higher investment return. The company wants to study cash flows to determine how much money it should keep in its checking accounts to pay claims. There are two types of claims: "repair" claims, and "totaled" claims. After reviewing historical data, the company has determined that the number of repair claims filed each week is a random variable that follows the probability distribution shown in the following table:

# Repair Claims 0 1 2 3 4 5 6 7 8 9 10 Probability 0.030 0.106 0.185 0.216 0.189 0.132 0.077 0.039 0.017 0.007 0.002

The company has also determined that the average cost per repair claim is normally distributed with a mean of $1,200 and standard deviation of $300 (with no negative values). To be clear, the costs of covering of each individual repair claim are not normally distributed; rather, the average cost per repair claim for a given week is normally distributed with a mean of $1,200 and a standard deviation of $300. In addition to repair claims, the company also receives claims for cars that have been "totaled" and cannot be repaired. There is a 15% chance of receiving one claim of this type in any week, and there is no chance of receiving more than one in any week. The cost for "totaled" cars is given by the following: $7500 * X, where X is a log-normal random variable with a mean parameter of 0.15 and a standard deviation parameter of 0.5.

Develop a descriptive model of this scenario; identify and name random and non-random variables along the way. You may develop a flowchart for yourself to help you visualize, but do not attach it to the submission. List all random variables, their distributions, and parameters. Code the model in Excel and replicate it 10,000 times. Answer the following questions What is the weekly average cost of all claims? Suppose that the company decides to keep $15,000 cash on hand to pay claims. What is the probability that this amount will not be adequate to cover claims in any given week?

1. Consider a monopolist who produces output Q under constant returns to scale, with marginal cost of 10. The monopolist produces during T > 2 periods. Demand for its product in each period is D(P) 2 100 2P, for P g 50. However, the monopolist 'does not know the demand at the outset' It only knows that the demand is linear and stationary. a. One recourse is for the monopolist to sample the market by announcing prices P1 and P2 in periods 1 and 2 and producing whatever quantities Q1 and Q2 consumers demand at these prices. It would then determine demand and behave optimally in subsequent periods. Show how this procedure works for the sample prices P1 = 20 and P2 = 40 and determine the optimal supply and pricing strategy for each period t > 2. (Assume there is no discounting of future prots.) ' b. An alternative recourse would be for the monopolist to hire a inarket research rm at a cost of s to determine the exact demand it faces. What is the value of knowing the exact demand prior to the commencement of operations (i.e., prior to period 1) rather than having to announce the sample prices P1 = 20 and P2 = 40 in periods 1 and 2? Would the rm be willing to pay an amount .3 up to this value? Is it capable of making this determination ex ante? Discuss. 0. Instead of announcing specic prices P1 = 20 and P2 = 40, suppose the monopo list were to draw prices randomly from a uniform distribution on the interval [10, 50]. Explain how to determine the rm's expected prot in the single period when it sets this randomly chosen price. Is the rm capable of performing this calculation ex ante? Explain. :1. Alternatively, suppose the rm knows that its demand is of the form D(P) = mP+ b. The rm believes that m and b are independently distributed; m has density function f on [1, 4] and b has density g on [80, 200]. In this case, write an expression for the irm's expected singleperiod prot from announcing price P. Write an expression for its axpected prot if it were to announce an optimal P. Is it capable of evaluating these? 3. Discuss how the sampling procedure described above involving one observation per )eriod might be generalized beyond the linear case to allow for an arbitrary demand :urve. What considerations might be relevant in deciding whether to hire a market 'esearch rm to determine the rm's demand? 3. Consider a pure exchange economy with two consumers and two goods. When con- :umer i consumes 51:37; 2 0 units of good 6, consumer 1 gets utility 5611 + (x21) and :onsumer 2 gets utility ($12) + $22 (93:31, where 6' 2 O and c' > O, \" 0 units of good 1 and consumer 2 owns 62 > 0 units of good 2. L. Describe in English the consumers' preferences and demand functions, being as spe :ic and complete as possible. For what goods might real consumers have preferences imilar to those in the model? ). What is the set of feasible allocations in this economy? 1 UNIVERSITY AT ALBANY, STATE UNIVERSITY OF NEW YORK DEPARTMENT OF ECONOMICS Ph.D. Preliminary Examination in Microeconomics, June 15, 2016 Answer any three of the following four numbered problems. Justify your answers whenever possible. Write your answer to each numbered problem in a. separate bluebook. Write the nurnber of the problem AND NOTHING ELSE on the cover of the bluebook. No electronic devices may be used. The exam lasts 4 hours. 1. Consider a monopolist who produces output Q under constant returns to scale, with marginal cost of 10. The monopolist produces during T > 2 periods. Demand for its product in each period is D(P) = 100 2P, for P S 50. However, the monopolist does not know the demand at the outset. It only knows that the demand is linear and stationary. a. One recourse is for the monopolist to sample the market by announcing prices P1 and P2 in periods 1 and 2 and producing whatever quantities Q1 and Q2 consuniers demand at these prices. It would then determine demand and behave optimally in subsequent periods. Show how this procedure works for the sample prices P1 = 20 and P2 = 40 and determine the optimal supply and pricing strategy for each period t > 2. (Assume there is no discounting of future profits.) ' b. An alternative recourse would be for the monopolist to hire a market research rm at a cost of .s- to determine the exact demand it faces. What is the value of knowing the exact demand prior to the commencement of operations (i.e., prior to period 1) rather than having to announce the sample prices P1 2 20 and P2 = 40 in periods 1 and 2? Would the rm be willing to pay an aniount 5' up to this value? Is it capable of making this determination ex ante? Discuss. c. Instead of announcing specic prices P1 = 20 and P2 = 40, suppose the monopo list were to draw prices randomly from a uniform distribution on the interval [10, 50]. Exp1ain how to determine the rm's expected prot in the single period when it sets this randomly chosen price. Is the rm capable of performing this calculation ex ante? Explain. (:1. Alternatively, suppose the rm knows that its demand is of the form D(P) = mP+ b. The rm believes that m and b are independently distributed; m has density function f on {1, 4] and b has density 9 on [80, 200]. In this case, write an expression for the rm's expected singleperiod prot from announcing price P. Write an expression for its expected prot if it were to announce an optimal P. Is it capable of evaluating these? e. Discuss how the sampling procedure described above involving one observation per period might be generalized beyond the linear case to allow for an arbitrary demand curve. What considerations might be relevant in deciding whether to hire a market research rm to determine the rm's demand? 2. Consider a pure exchange economy with two consumers and two goods. When con sumer z' consumes xei Z 0 units of good Z, consumer 1 gets utility $11 + 45012;) and consumer 2 gets utility (:L-12) + 9322 9:531, where 6 Z O and 45' > O, >\" 0 units of good 1 and consumer 2 owns e2 > 0 units of good 2. a. Describe in English the consumers' preferences and demand functions, being as spe~ cic and complete as possible. For what goods might real consumers have preferences similar to those in the model? b. What is the set of feasible allocations in this economy? 1 mers consume positive amounts of both goods). In what way does this set depend on Starting from a PE allocation, does a small transfer of good 1 from consumer 1 to nsumer 2 leave the allocation Pareto efficient? Let 0 = 0. Characterize a competitive (Walrasian) equilibrium (CE) for this economy. the allocation Pareto efficient? Let 0 - 1/2. Characterize a CE when consumer 2 acts as if the equilibrium consump- on of good 2 by consumer 1 is fixed, unaffected by actions of consumer 2. Under what, if any, condition is the CE allocation in part e Pareto efficient? Is it possible that in the CE allocation in part e consumer 1 consumes inefficiently tle of good 2, given consumer l's consumption of good 1? Consider the case in which t) = In t. Explain and interpret your answer. A government devises an optimal tax schedule for a population, half of whom are of pe H, half of type L. A type H agent produces qu = 2ex units of output (income) en it provides en E (0, 1] units of effort. A type L agent produces q = (3/2) ez units of tput when it provides ez E [0, 1] units of effort. Outputs produced by different agents e physically homogeneous, hence indistinguishable, and (except in part a, below) the vernment cannot directly observe the type of any particular agent or its effort level. he government observes agents' incomes (outputs) and assigns a tax to each income el. The government knows that if a type i agent produces qi units of output, providing units of effort and paying t;