Consider the production function f(E) = 2E - E2 where E denotes the level of a marketing agent’s effort at selling your novel. Assume the agent’s costs of effort is C = 4E. With an output price of p = 1, determine the level of effort, E, along with the profits for the principal (you) and the agent for each of the following situations:
a. Fixed Compensation: the agent receives a payment of $160.
b. Residual Claimant: the agent pays you a franchise fee of $64 and then runs the business herself and keeps the profits of the company
c. Sharecropping: the agent receives a 50% share of the output.