Source: Microeconomic Theory, Texas A&M University
Tags: profit maximisation, marginal revenue, marginal cost, MR=MC, marginal profit, franchise, franchisor, franchisee, revenue maximisation, Burger King, optimal output, ECO 101
A firm maximises profit by producing where marginal revenue equals marginal cost (MR = MC), which is equivalent to saying marginal profit equals zero. Franchise relationships create a tension: the franchisee wants to maximise profit, while the franchisor (parent company) wants to maximise revenue, because the royalty is a percentage of revenue. This difference in objectives leads to disagreements about pricing and output.
Marginal revenue (MR)
The additional revenue from a one-unit increase in output sales.
Marginal cost (MC)
The additional cost of producing one more unit of output.
Marginal profit
How much profit increases when you increase output (Q) by one unit. Equivalently, marginal profit = MR − MC.
Profit-maximising output
The quantity where marginal profit equals zero, or equivalently where MR = MC.
Franchisor (parent company)
The company that owns the brand and grants franchise rights. Collects a fixed percentage of the franchisee's revenue as a royalty.
Franchisee (individual operator)
The individual or business that pays for the right to operate under the franchisor's brand. Wants to maximise profit, not revenue.
Revenue-maximising output
The quantity where MR = 0 (total revenue is at its peak). This is typically a higher output level than the profit-maximising output.
Pure selling problem
A situation where variable costs are zero or so low they can be ignored. The firm's optimisation problem reduces to maximising revenue.
To maximise profit, set output where MR = MC.
At that point, marginal profit is zero (the slope of the profit function is zero).
If marginal profit is positive (MR > MC), the firm should increase output, because each additional unit adds to profit.
If marginal profit is negative (MR < MC), the firm should reduce output until marginal profit returns to zero.
Example: π = −200 + 80Q − 0.2Q²
Take the first derivative with respect to Q: dπ/dQ = 80 − 0.4Q.
Set equal to zero: 80 − 0.4Q = 0, so Q = 200.
The profit-maximising output is Q = 200.
This same structure appears with slight variations (e.g. π = −200 + 8Q − 0.2Q²). The method is always the same: differentiate, set to zero, solve for Q.
To sell more units, the firm must lower its price. This is the defining feature of a downward-sloping demand curve.
MR is less than price for every unit after the first, because lowering the price to sell one more unit also reduces revenue on all previous units.
To produce more units, the firm needs to raise its prices (or, more precisely, higher prices are needed to cover rising marginal costs of production).
Higher wages (costs rise):
The firm's marginal cost curve shifts up.
Optimal output falls; the firm's price rises.
Summary: price increases, output decreases.
Lower wages (costs fall):
The firm's marginal cost curve shifts down.
Optimal output rises; the firm's price falls.
Summary: price decreases, quantity increases.
General rule: a firm's optimal price and quantity change when its variable costs change.
Methods that work for all firms include setting MR = MC and using the profit equation's first-order condition.
Setting MR = 0 is not a general method for all firms. MR = 0 gives you the revenue-maximising output, which only coincides with the profit maximum when variable costs are zero (a pure selling problem).
The franchisor collects a fixed percentage of the franchisee's revenue. This creates a structural conflict:
The franchisee wants to maximise profit (revenue minus all costs, including the royalty).
The franchisor wants to maximise revenue, because its royalty income is proportional to revenue.
Consequences:
The franchisee's revenue-maximising output is greater than its profit-maximising output (because revenue peaks at a higher quantity than profit does when costs are positive).
The franchisee favours raising prices on best-selling items (to increase margin per unit).
The franchisor would prefer lower prices and higher volume (to increase total revenue).
What the franchisee gets from the parent company:
Brand recognition, marketing, supply chain, operational systems. The claim that the franchisee "gets no benefits" from the parent company is false.
The claim that the franchisor "exploits" the franchisee by giving them little is also false in this framing.
Condition | Meaning |
|---|---|
MR = MC | Profit-maximising output |
MR = 0 | Revenue-maximising output |
Marginal profit = 0 | Same as MR = MC; slope of profit function is zero |
dπ/dQ = 0 | First-order condition for profit maximisation |
Profit function template: π = −F + aQ − bQ², where F is fixed cost, a is the linear revenue/cost coefficient, and b governs the curvature.
dπ/dQ = a − 2bQ = 0
Q* = a / (2b)
⚠️ "MR = MC" and "marginal profit = zero" are two ways of saying the same thing. The exam may use either phrasing.
⚠️ If marginal profit is positive, increase output. If marginal profit is negative, decrease output. This is tested directly.
⚠️ Know the franchise conflict cold: franchisee maximises profit, franchisor maximises revenue. Expect a question that asks you to fill in the blanks.
⚠️ A change in variable costs changes the firm's optimal P and Q. A change in fixed costs alone does not (fixed costs drop out when you differentiate).
⚠️ In a pure selling problem, variable costs are zero, so the firm maximises revenue (MR = 0).
Q: To maximise profit, a firm should set output where what condition holds?
A: Marginal revenue equals marginal cost (MR = MC).
Q: If a firm's marginal profit is positive at its current output, what should it do?
A: Increase output, because MR is greater than MC.
Q: If a firm's marginal profit is negative at its current output, what should it do?
A: Reduce output until marginal profit equals zero.
Q: Given π = −200 + 80Q − 0.2Q², what is the profit-maximising output?
A: Q = 200 (take the derivative, set to zero, solve).
Q: In a franchise, who wants to maximise revenue and who wants to maximise profit?
A: The franchisor (parent company) wants to maximise revenue. The franchisee (individual operator) wants to maximise profit.
Q: Who favours raising prices on best-selling items, the franchisor or the franchisee?
A: The franchisee.
Q: A firm negotiates higher wages. What happens to its price and output?
A: Price increases and output decreases.
Q: What is a pure selling problem?
A: A situation where variable costs are zero or negligible, so the firm's problem reduces to maximising revenue.
Q: True or false: the franchisee's revenue-maximising output is greater than its profit-maximising output.
A: True.
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