1)A Consumer Always Spends 40% of His Income on Good X and the Remainder on Good Y. The

1)a consumer always spends 40% of his income on good x and the remainder on good y. The price elasticity of the demand for both x and y will be unity. True or False? Explain your answer (15marks)

2)Lynne’s income is £2, 000 and she is risk averse. The probability of someone slipping on her stairs is 1/8 . If this happens, she will be sued for £1, 000 and will have to pay that amount. She can purchase insurance at a price of £0.30 per pound of coverage.
a) use the contingent commodity framework with consumption if not sued on the horizontal axis and consumption if sued on the vertical axis and illustrate lynnes situation before an accident happens (10marks)
b)Show in your graph how the equilibrium amount of insurance coverage is determined (15marks)
c)Show how it changes if the probability of someone slipping increases to 1/4 , but the premium is unchanged. (15marks)

3)consider two individuals M and F who must split 20 units of good X and 10 units of good Y. Suppose we can represent M's preference with the utility function
Um =X^2mYm
and Fs preference with the utility
Uf = min{Xf, 2Yf}
where Xm and Xf indicate their X consumption, while Ym and Yf indicate their Y consumption
a) derive the MRS for M (10 marks)
b) Interpret F's utility function (10marks)
c) find and graph the contract curve (20 marks)
d) what is the ratio of the price of X to the Price of Y in competitive equilibrium (10 marks)
e) to which allocation will M and F trade? indicate this outcome clearly in your graph (15 marks)

4)Assume that in the market there exist two types of workers where the principle cannot distinguish types. The two types only differ with respect to the disutility of effort. The disutility is either e^2 or 2e^2.
The utility function for worker one is
U^1(w,e) = w - e^2
and for worker two
U^2(w,e) = w - 2e^2
both types of workers have reservation utility zero
the probability that the worker is of type 1 is q = 1/2
an intrested firm is risk neutral and has profits Π(w,e) = e - w
a) which is the good high productive worker and which is the low productive worker (5 marks)
b)derive the optimal contract for the firm if it had perfect info about the workers type. what effort levels are demanded and what wages paid. calculate the firms profits of both types were employed (15 marks)
c) formulate the problem when an adverse problem is present (10 marks)
d) dervive the second best contract and calculate the firms profits (15 marks)
e) compare the cases of symmetric and assymetric info (10 marks)