Question

Case 5.0: Incentives in the Firm – Compensating the CEO

Let’s work through an incentive concept and problem. “Moral hazard” problems arise when someone – the “principal” – hires an agent to do something, but the agent has an incentive to do something else. For example, firm owners may want their management team to maximize profits, but maximizing profits is hard, time-consuming work that could interfere with the management team’s preference for playing golf. If top management simply receives a salary, the problem is aggravated because the managers may not be motivated to satisfy the owners, and the owners can’t easily monitor management activity to know if they’re really doing a good job. The problem is resolved in large part if the owners tie most or all of management compensation to firm profits, as income is often a pretty good motivator (although some golf nuts will still pause for a while over this one.) We can set up a scenario to explore this incentive issue further, and this problem will also help fix in our minds the difference between maximizing revenue and maximizing profit.

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. 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. (Hint: basing compensation on revenue will motivate revenue maximization rather than profit maximization!)

1.    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:

2.    Suppose you are asked to mediate in the negotiations. Can you propose an incentive-based compensation scheme for the CEO that both parties are likely to accept, assuming everyone would like to maximize their income?

Your proposal:

Demonstration that everyone is better off than under their own proposal and thus should accept your proposal:

Firm price:
Firm output:
Total revenue:
Firm profit:
CEO compensation:
Remaining profit for owners:

3.    Now thinking even more shrewdly: what’s the maximum price you could charge for your consulting services and still leave everyone better off?

$

Answer 1

CEO Proposal: 20% of TR; The revenue will be maximised at MR = 0 or 100-2Q = 0 or Q = 50. At this level:

Firm Price : P = 100-50 = 50

Firm Output = 50

TR = P*Q = 50*50 = 2500

Firm Profit = TR-TC = 2500 - 0.5 * (50)² = 1250 (ideally the CEO compensation should be deducted from this profit number but for the sake of this problem it is shown seprately)

CEO Compensation = 20% * 2500 = 500

Remainig profit for owners = 1250-500 = 750

Owner's Proposal: 10% of TR; At Q=50, we will have:

Firm Price : P = 100-50 = 50

Firm Output = 50

TR = P*Q = 2500

Firm Profit = TR-TC = 1250 (ideally the CEO compensation should be deducted from this profit number but for the sake of this problem it is shown seprately)

CEO Compensation = 10% * 2500 = 250

Remainig profit for owners = 1250-250 = 1000

2. As we see that CEO looses when the revenue percentage incentive decreases from 20% to 10% and the owner gains by same proportion. Instead they can look at profit maximisation and we can look at 22.5% CEO incentive at this level:

Profit Maximisation output : MR = MC ; 100-2Q = Q or Q = 33.33

Firm Price : P = 100-100/3 = 66.67

Firm Output = 33.33 (we have consioucly not rounded to whole number)

TR = P*Q = 66.67*33.33 = 2222.22

Firm Profit = TR-TC = 2222.22 - 0.5 * (33.33)² = 1666.67 (ideally the CEO compensation should be deducted from this profit number but for the sake of this problem it is shown seprately)

CEO Compensation = 22.5% * 2222.22 = 500

Remainig profit for owners = 1666.67-500 = 1166.67

We see that in this case the CEO makes more money than under the 10% incentive plan and same as under the 20% incentive plan but still the owners will have higher profit than either case. Hence this plan should be acceptable to both.

3. Since the above proposal still leaves (1166.67 - 1000) = 166.67 as extra profit for the owners, assuming the CEO is capped at 22.5% or 500, hence that is the maximum price we can charge for the assignment. At this level both the stakeholders should be equivocal.