Question 1

1.Sarada operates an essay proofreading service. She hires graduate students from the English Department to do the proofreading. Sarada's utility function is where denotes pages and is the cost per page. There are two types of student who apply to work for Sarada: high productivity students who can proofread and correct 12 pages per hour, and low productivity students who can read and correct 8 pages per hour. All students have the same preferences, with utility linear in income; 1/4 of the applicants have high productivity. Each student's best alternative job pays $16 per hour. a) Assuming students can be employed in their alternative job for fractions of an hour, what is the opportunity cost of a page to a high productivity worker? Of a low productivity worker? (Show your calculations for this.) Suppose Sarada has all the bargaining power and can costlessly observe eaca student's type. b) How many pages per hour would be required from a high productivity worker? From a low productivity worker? (Show your calculations.) c) Describe the contract students of each type would be offered. Let denote the number of pages and the payment per page in the contract for a low productivity worker and denote those values in the contract for a high productivity worker. Unfortunately Sarada cannot costlessly observe anyone's type even though she knows that each applicant knows their own type. d) Which contract would each applicant choose if the contracts in (c) were offered? Why? e) Briey explain the constraints the contract for each type must satisfy to provide an incentive for high and low productivity workers to choose different contracts. 1) Which type of student receives \"information rents\" under the equilibrium contract under asymmetric information? Who bears the cost of these rents? g) How would the information rents be affected if Sarada were unwilling to hire low productivity students