Worked example 1

A monopolist faces P = 40 − Q and TC = 200 + 8Q.

(a) Find output and price for profit maximisation (MC = MR). (b) Find output and price for revenue maximisation (MR = 0). (c) Explain why a manager might prefer (b).

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(a) Profit max: MR = 40 − 2Q, MC = 8 40 − 2Q = 8 → Q = 16, P = 40 − 16 = £24 Profit = (24 × 16) − (200 + 128) = 384 − 328 = £56

(b) Revenue max: MR = 0 → 40 − 2Q = 0 → Q = 20, P = £20 TR = 20 × 20 = £400 (maximum) Profit = 400 − (200 + 160) = £40 (lower than profit max)

Manager's bonus tied to sales revenue, not profit.
Higher output (20 vs 16) means larger market share and greater perceived success.
Satisficing: shareholders get adequate profit (£40 > 0) while manager maximises personal reward linked to turnover.
Short-run sacrifice of £16 profit may be justified by manager's career incentives.

Worked example 2

A firm's cost and revenue data is shown in the table below. Use the data to identify the output and price for different company objectives.

Output (units)	Price ($)	Total Cost ($)
10	28	150
---	---	---
20	26	280
30	24	420
40	22	600
50	20	850
60	18	1200

Show solution outline

First, we need to calculate Total Revenue (TR), Profit (TR-TC), and Average Cost (AC) to analyse the different objectives.

Step 1: Calculate TR and Profit

TR = Price x Output
Profit = TR - TC

Output (Q)	Price (AR) ($)	TR ($)	TC ($)	Profit ($)
10	28	280	150	130
---	---	---	---	---
20	26	520	280	240
30	24	720	420	300
40	22	880	600	280
50	20	1000	850	150
60	18	1080	1200	-120

Step 2: Identify the Profit Maximising Output Profit is maximised where the difference between TR and TC is greatest. From the table, the highest profit is $300, which occurs at an output of 30 units and a price of $24.

Step 3: Identify the Revenue Maximising Output Total Revenue is maximised at the highest value before it starts to decline. Based on the data, TR is still increasing at 60 units. A revenue-maximising firm would continue to expand output as long as Marginal Revenue (MR) is positive. At 60 units, TR is $1080. Since the data does not show TR falling, the revenue-maximising output is at least 60 units.

Step 4: Identify the Sales Maximising Output (AC=AR) This objective aims to sell as many units as possible without making a loss (i.e., where Profit ≥ 0 or AR ≥ AC). We need to calculate Average Cost (AC = TC/Q).

| Output (Q) | Price (AR) ( $) | AC ($ ) | Profit ( $) |$ |---|---|---|---|

10	28	15.00	130
20	26	14.00	240
30	24	14.00	300
40	22	15.00	280
50	20	17.00	150
60	18	20.00	-120

At 50 units, the firm makes a profit of $150 (AR=$ 20, AC=$17). At 60 units, it makes a loss of $120 (AR= $18, AC=$ 20). A sales-maximising firm would produce the highest output without making a loss. Therefore, the sales-maximising output is 50 units at a price of ** $20**.$

Firms' costs, revenue and objectives — practice questions

Worked example 1

Worked example 2