2. Suppose, as in class, that the utility function of a worker is U(w, e)=√w-e, where w is the wage and e € {0,.8} is the level of effort. Suppose the reservation utility is 1. Suppose the outcome is $10 or $0 and that the probability of the $10 outcome is .6 if the worker works hard and .2 if the worker chooses low effort. (a) If you could costlessly monitor the worker's effort, would you want the worker to work hard? What payments would you offer and for what effort?

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Consider the representative consumer who decides consumption and leisure. Theenvironment is the same as in Lecture 5. Keep the same notation. The preference is givenby U (C,L) = αln C + (1 −α) ln L. Assume h = 1, i.e., the time endowment is one day.(a) Write down the utility maximization problem.(b) Derive the demand for consumption and the supply for labour.(c) Suppose the non-wage income π −T increases while the wage rate w falls at the sametime. The size of the changes can be different. Determine the effects on consumptiondemand and labour supply (i.e., leisure demand). Use the indifference map to explainyour results in terms of income and substitution effects for the following cases:(i) The increase in π −T exactly cancels out the drop in w, i.e., |∆ (π −T)|= |∆w|.(ii) The increase in π −T is greater than the drop in w, i.e., |∆ (π −T)|> |∆w|.(iii) The increase in π −T is smaller than the drop in w, i.e., |∆ (π −T)|< |∆w|.(d)  Suppose the utility function is Cobb-Douglas: U…

Assume, in producing one unit of a good X, an agent can exert either the good effort (G) or the bad effort (L), which cause production defects with probability 0.25 or 0.75 respectively. His utility function in effort e and wage w is U(w, e) = 100 (10/w) c(e) where c(G) = 2 for the good effort and c(L) = () for the bad effort. Production defects are contractible and so can be included in the agent's contract, but effort is not contractible. Good X sells for $20 if there are no defects and $0 otherwise. The principal is risk-neutral and likes profit. Assume the agent has a reservation utility/outside option of U=0. If effort is not contractible then:: Select one: O a. There is insufficient information to know the principal's choice of contract because we do not know the agent's level of absolute risk aversion. O b. the principal will be indifferent between writing a contract to achieve the good effort level and writing a contract to achieve the bad effort level O c. the principal will…

7. A firm's can sell higher quality products for more: P = 10 + 20 X, where X is the quality of the product sold. Workers hired by the firm make a product, the quality of which depends on effort and luck X = e +€, where X= Quality, e = effort, and e = Luck E(e) = 0. .so average quality depends on effort Wages are contingent on outcome (X) where w = C(e) = e² with e20 10 + 8 X and the cost of effort Determine the level of effort, the expected wage, and the expected profit for the above wage arrangement. Compare your results to the case where workers are paid a standard wage of $10 and the level of effort and the quality of the product do not alter the wage.

advanced microeconomics, principal agent

Persons A and B are roommates. Person A smokes and Person B does not. The index s measures how smoky the room is. It varies from s=0, when there is no smoke in the room, to s=1, when the room is filled with smoke. Thus, 1-s measures how "clean" the air in the room is. Person A's utility function is ua(XA,s)=Xa.S, where xA is the amount of money Person A owns. Person B's utility function is ug(xg, 1s)=Xg .(1-s)³, where xg is the amount of money Person B owns. Each person starts with an endowment of 5 units of money. Person A has the legal right to a fill up the room with smoke and there exists a market for smoke "abatements". At the Walrasian equilibrium, how much money will person B be left with? а. Хв31.25 ОБ. Хв32.25 O c. XB=0.25 O d. Xg=0.25 е. None of the other answers.

Choice under uncertainty. Consider a coin-toss game in which the player gets $30 if they win, and $5 if they lose. The probability of winning is 50%. (a) Alan is (just) willing to pay $15 to play this game. What is Alan’s attitude to risk? Show your work.(b) Assume a market with many identical Alans, who are all forced to pay $15 to play this coin-toss game. An insurer offers an insurance policy to protect the Alans from the risk. What would be the fair (zero profit) premium on this policy?   i need help with question B please.

Rachel's objective is to maximize the expected profit, subject to that Emma works for Rachel and Emma puts effort. However, effort level is not observable. Hence, Rachel needs to write a contract based on the observables. Let's say, Rachel pays Emma based on the outcome: when the profit is $0, 2 when the profit is $2000, and zu when the profit is $3,000. Then Emma has three options: (i) Not to work for Rachel (ii) Work for Rachel without effort (iii) Work for Rachel with effort Find Emma's expected utility on each option.

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