# Quiz 18: Asymmetric Information

a) If the contingency fee is 1/3 rd , the surplus to the lawyer is given by  The first order condition for the above function is Hence, the surplus maximizing effort for the lawyer is The lawyer's surplus then is The plaintiff's surplus then is b) If the contingency fee is c , the surplus to the lawyer is given by  The first order condition for the above function is Hence, the surplus maximizing effort for the lawyer is The lawyer's surplus then is The plaintiff's surplus then is c) The plaintiff's surplus is The first order condition for the above function is Hence, the surplus maximizing contingency fee for the plaintiff is The plaintiff's surplus then is If contingency fees is , surplus maximizing effort for the lawyer is The lawyer's surplus then is d) If the plaintiff can sell the case to her lawyer she can extract the whole surplus of the lawyer and increase her surplus. This can be done by setting a 100% contingency fee. The lawyer will then choose l = 1 and earn a surplus ½. The plaintiff can then sell the case for ½ and extract his surplus. As this scheme does not leave the lawyer with any surplus it is outlawed in many countries.
If instead of two tariffs, the coffee shop charges price p per ounce of coffee, then the the utility function of a consumer is given by The first order condition for the above yields So, the inverse demand function of consumer is given by As , we get Putting this in the inverse demand function, we get So, The expected profit of the coffee shop is given by Substituting the demand function for the two types of demanders, we get  The first order condition for this is Re arranging the above we get, Solving for p, we get, The expected profit of the shop is given by If instead the firm sets non-linear price, the expected profit is found to be 50. Hence, non-linear price is a better strategy.
a) We know that to maximize the monopolists' expected profit As , we get Substituting the values, we get     The tariff for the low type is given by The optimal quantity and tariff for high demander remains unchanged at 16 and 160 respectively. Only the quantity and tariff of the low type is affected, that of the high type remains unaffected. This shows that there is "no distortion at the top".