question archive A small firm faces an inverse demand function of P = 120 - 2Q
A small firm faces an inverse demand function of P = 120 - 2Q
Subject:EconomicsPrice: Bought3
A small firm faces an inverse demand function of P = 120 - 2Q. Its total cost function is given by TC = Q2. (You should see right away that marginal revenue is thus MR = 120 - 4Q, and it also happens that marginal cost is MC = 2Q. MR and MC are the first derivatives of total revenue and total cost, respectively.
The Chief Executive Officer will manage the firm, choosing output and price. Currently, the CEO is negotiating an incentive-based contract with the shareholders of the company. The CEO has proposed that she get 20% of the total revenue brought in by the firm. The shareholders' representative has counter-offered that 10% of total revenue be given to the CEO.
How much income will each plan generate for the CEO and for the shareholders, respectively? (Hint: since both plans create incentives for the CEO to maximize revenue rather than profit, you should not set MR = MC at this point. BIG hint: revenue is maximized when selling an additional unit won't increase your revenue, or in math terms, when MR = 0.)
CEO's proposal: she keeps 20% of TR.
Firm price:
Firm output:
Total revenue:
Firm profit:
CEO compensation:
Remaining profit for owners:
Owners' proposal: CEO keeps 10% of TR.
Firm price:
Firm output:
Total revenue:
Firm profit:
CEO compensation:
Remaining profit for owners:
