One firm is owner managed. The quantity decision for this firm is made by the owner, who retains any profits. This owner is risk neutral.
The second firm is not managed by its owner. The owner of the second firm has hired a manager and has given this manager a contract wherein the compensation paid to the manager is a linear function of the profits the firm shows, 1r, and the quantity that the firm sells, x2 • Specifically, this contract calls for the manager to be paid a1r + f)x2 , where a and fJ are given constants. The owner retains any profits made by the firm, net of pay to the manager. Note well that the manager makes the quantity decision and not the owner, and the manager does so to maximize her compensation and not the net profits of the owner.

(a) What, in this case (for given a and f}), is the Cournot equilibrium in the market? What (as a function of a and fJ ) are the profits of the first firm, the managers compensation, and the net profits (to the owner) of the second firm?

(b) The owner of the second firm is interested in designing the "optimal" contract for her manager. The contract must, in equilibrium, provide the manager with a reservation level of income Y . Other than that, the owner can choose any linear contract she wishes; a and fJ are chosen to maximize her net (after compensation) profits. The owner-manager of the first firm and the manager of the second firm will behave in Cournot fashion after this contract is chosen. If you are worried about such things, the owner­ manager of the first firm will know the contract terms under which the manager of the second firm operates. What is that optimal contract? (Hint: Draw pictures!)

(c) Suppose now that both firms are managed by managers distinct from owners, both managers are paid according to contracts that have compensation linear in profits and sales quantity, and both managers have a reservation level of compensation that must be met. The two owners simultaneously and independently set the terms for their managers' (re­ spective) contracts. What will be the equilibrium in this game?

(d) We can imagine, in (c), many possible ways this game is played. Here are two extremes.