Profit maximisation as the main objective of a firm

Types of Cost, Revenue and Profit

Cost

Imagine you run a lemonade stand. Some costs stay the same no matter how many cups you sell (like the cost of the stand itself). Other costs change with sales (like lemons and sugar).

• Fixed Cost (FC): Cost that doesn’t change with output. Example: Rent for the stand. $FC = \$50$ per day.
• Variable Cost (VC): Cost that changes with output. Example: Lemons, sugar, cups. $VC = \$0.50 \times Q$.
• Total Cost (TC): Sum of fixed and variable costs. $TC = FC + VC$.
• Average Cost (AC): Cost per unit. $AC = \frac{TC}{Q}$.
• Marginal Cost (MC): Extra cost of producing one more unit. $MC = \frac{dTC}{dQ}$.

Revenue

Revenue is the money you get from selling your lemonade.

• Total Revenue (TR): Price × Quantity. $TR = P \times Q$.
• Average Revenue (AR): Revenue per unit. $AR = \frac{TR}{Q}$ (in perfect competition, AR = P).
• Marginal Revenue (MR): Extra revenue from selling one more unit. $MR = \frac{dTR}{dQ}$.

Profit

Profit is what you keep after paying all costs.

• Total Profit (π): $π = TR - TC$.
• Average Profit (πₐ): Profit per unit. $πₐ = \frac{π}{Q}$.
• Marginal Profit (πₘ): Extra profit from one more unit. $πₘ = MR - MC$.

Short‑Run and Long‑Run Production

Short‑Run (SR)

In the short‑run, at least one input (like the stand) is fixed. You can only change variable inputs (lemons, sugar).

• Capacity is limited by the fixed input.
• Firms can experience economies or diseconomies of scale within this limited capacity.
• Decision: How many cups to produce given the fixed cost.

Long‑Run (LR)

In the long‑run, all inputs are variable. Firms can change the size of the stand, buy new equipment, or even exit the market.

• Capacity can be increased or decreased.
• Firms choose the most cost‑efficient scale of production.
• Decision: What scale of output gives the lowest average cost.

Profit Maximisation: The Firm’s Main Objective

Firms aim to make the most profit possible. The key rule is:

$MR = MC$

Where Marginal Revenue (MR) equals Marginal Cost (MC). If MR > MC, produce more; if MR < MC, produce less.

Perfect Competition

The firm is a price taker: $P = AR = MR$.

• Profit maximisation occurs where $P = MC$.
• In the long run, firms earn zero economic profit ($π = 0$).

Monopoly

The firm can set price. It chooses output where $MR = MC$ and then charges the highest price consumers are willing to pay.

• Profit maximisation leads to higher price and lower output than in competition.
• Can earn positive economic profit in the long run.

🔍 Quick Check: If a firm’s marginal cost curve rises steeply after a certain output, it should stop producing more because $MC$ will exceed $MR$ and profit will drop.

💡 Remember: Profit maximisation is about balancing the extra revenue from selling one more unit against the extra cost of producing that unit. The sweet spot is where they are equal.