Objectives, decision conditions and agency
| English | 中文 | Pinyin |
|---|---|---|
| satisficing/ˈsætɪsfɪsɪŋ/ | 满意化决策 | mǎn yì huà jué cè |
| principal-agent problem/ˈprɪnsɪpl ˈeɪdʒənt ˈprɒbləm/ | 委托代理问题 | wěi tuō dài lǐ wèn tí |
A decision you can investigate
- A manager rewarded for sales may choose a different output from an owner rewarded for profit. A business may instead meet a satisfactory profit target while protecting service quality.
- Identify the objective before calling an output decision optimal.
Build the explanation
- Profit maximization seeks the largest TR−TC, including relevant opportunity costs. In a differentiable interior model, MR=MC is the candidate condition; marginal profit must change from positive to negative or the global choices must be compared. Revenue maximization seeks the largest TR; the interior condition MR=0 needs a maximum and feasible demand. Sales-volume maximization seeks the greatest feasible Q under a stated constraint: with a normal-profit constraint this often lies where TR=TC, or AR=AC, on the high-output break-even boundary. Without that constraint the decision is different.
- Satisficing 满意化决策 means achieving an acceptable target rather than maximizing one measure; multiple goals, limited information and stakeholder duties can motivate it. Separation of ownership and control creates a principal-agent problem 委托代理问题 when managers’ incentives or information differ from owners’ interests. Pay, oversight and governance can reduce conflicts but introduce costs or encourage narrow measured targets.
Work through the evidence
- Use a fictional continuous-output model: P=100−Q, TR=100Q−Q², TC=200+20Q, with cost including the required normal return and Q between 0 and 100. MR=100−2Q and MC=20. Profit maximum occurs at Q40: price60, TR2400, TC1000, profit1400. Revenue maximum occurs at Q50: price50, TR2500, TC1200, profit1300.
- For sales maximization subject to non-negative economic profit, solve 100Q−Q²=200+20Q, so Q²−80Q+200=0. Roots are approximately 2.5834 and 77.4166; choose the larger feasible boundary, Q77.4166, with price22.5834 and economic profit0. A revenue-focused manager chooses more output than the profit-focused owner here. A satisficing target profit1200 could be met by several outputs; it does not identify a unique maximum.
What is profit at Q40?
TR2400−TC1000=1400.
Which output maximizes stated revenue?
MR=100−2Q=0 gives the concave TR maximum Q50.
Any point satisfying MR=MC must be a profit maximum in every model.
Check the direction of marginal-profit change, feasibility and alternative boundaries.
Test the limits
- The formula conditions require the model’s differentiability, feasibility and cost definitions. MR=MC is not sufficient for a maximum if it occurs at a minimum or an inferior boundary. Integer production, capacity constraints and discontinuous costs require direct comparison. Sales maximization without the normal-profit constraint can reach another boundary, so never state AR=AC as a universal rule for selling most units.
- The normal return is inside economic costs; zero economic profit is not necessarily zero accounting profit. Not-for-profit/public/member enterprises can choose different purposes. Bonus schemes based only on revenue can encourage costly sales or misleading reporting; a balanced governance arrangement needs evidence of service, risk and longer-term outcomes. The fictional equations are not a forecast or a business recommendation.
What constraint makes the high break-even root relevant to sales maximization?
The greatest feasible quantity under TR≥TC lies at the high-output break-even boundary here.
Apply and explain your answer
- Why is Q50 optimal for revenue but not for profit in this case?
- TR is largest at Q50, but the extra output raises costs enough that profit1300 is below the Q40 maximum1400. The objective changes the chosen quantity.
Match the terms to their meanings.
Use each term for its stated economic relationship.
Use the terms precisely
- satisficing: Choosing an outcome meeting an acceptable target rather than maximizing one measure.
- principal-agent problem: A conflict arising when an agent’s incentives or information differ from the principal’s interests.
Use a fictional continuous-output model: P=100−Q, TR=100Q−Q², TC=200+20Q, with cost including the required normal return and Q between 0 and 100. MR=100−2Q and MC=20. Profit maximum occurs at Q40: price60, TR2400, TC1000, profit1400. Revenue maximum occurs at Q50: price50, TR2500, TC1200, profit1300. For sales maximization subject to non-negative economic profit, solve 100Q−Q²=200+20Q, so Q²−80Q+200=0. Roots are approximately 2.5834 and 77.4166; choose the larger feasible boundary, Q77.4166, with price22.5834 and economic profit0. A revenue-focused manager chooses more output than the profit-focused owner here. A satisficing target profit1200 could be met by several outputs; it does not identify a unique maximum.
The formula conditions require the model’s differentiability, feasibility and cost definitions. MR=MC is not sufficient for a maximum if it occurs at a minimum or an inferior boundary. Integer production, capacity constraints and discontinuous costs require direct comparison. Sales maximization without the normal-profit constraint can reach another boundary, so never state AR=AC as a universal rule for selling most units. The normal return is inside economic costs; zero economic profit is not necessarily zero accounting profit. Not-for-profit/public/member enterprises can choose different purposes. Bonus schemes based only on revenue can encourage costly sales or misleading reporting; a balanced governance arrangement needs evidence of service, risk and longer-term outcomes. The fictional equations are not a forecast or a business recommendation.
Profit maximization seeks the largest TR−TC, including relevant opportunity costs. In a differentiable interior model, MR=MC is the candidate condition; marginal profit must change from positive to negative or the global choices must be compared. Revenue maximization seeks the largest TR; the interior condition MR=0 needs a maximum and feasible demand. Sales-volume maximization seeks the greatest feasible Q under a stated constraint: with a normal-profit constraint this often lies where TR=TC, or AR=AC, on the high-output break-even boundary. Without that constraint the decision is different.