A small firm faces an inverse demand function of P = 100 - Q. Its total cost function is given by TC = .5Q2. (You should see right away that marginal revenue is thus MR = 100 - 2Q, and it also happens that marginal cost is just MC = Q. Both MR and MC are the first derivatives of total revenue and total cost. And a quick comment on MC: unlike some marginal cost functions we've seen, this one is not constant, because marginal cost is getting $1 higher with each additional unit of output.)
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.
(Hint: basing compensation on revenue will motivate revenue maximization rather than profit maximization!)
Hint: since the plan creates 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.)
Owners' proposal: CEO keeps 10% of TR.
Firm price:
Firm output:
Total revenue:
Firm profit:
CEO compensation:
Remaining profit for owners:
A small firm faces an inverse demand function of P = 100 - Q. Its total cost function is given by TC = .5Q2. (You should see right away that marginal revenue is thus MR = 100 - 2Q, and it also happens that marginal cost is just MC = Q. Both MR and MC are the first derivatives of total revenue and total cost. And a quick comment on MC: unlike some marginal cost functions we've seen, this one is not constant, because marginal cost is getting $1 higher with each additional unit of output.)
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.
(Hint: basing compensation on revenue will motivate revenue maximization rather than profit maximization!)
Hint: since the plan creates 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.)
Owners' proposal: CEO keeps 10% of TR.
|
Firm price: |
|
|
Firm output: |
|
|
Total revenue: |
|
|
Firm profit: |
|
|
CEO compensation: |
|
|
Remaining profit for owners: |
