Price Sensitivity and Profit Curves
You are modeling a single network service with a per-unit price p offered to a large market. Customer demand decreases with price. Assume a standard downward-sloping demand curve, constant marginal cost c per unit, optional fixed cost F, and no capacity constraints.
Constraints & Assumptions
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Use a demand curve such as Q(p) = a - b p for illustration if needed.
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Keep price, quantity, revenue, cost, and profit definitions separate.
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Explain the shape of the curves rather than only drawing them.
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Note feasibility constraints such as nonnegative demand.
Clarifying Questions to Ask
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Is the demand curve estimated from historical data, experiments, or assumptions?
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Is marginal cost constant across all quantities?
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Is the goal to maximize profit, revenue, adoption, or market share?
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Are there competitor, regulatory, or capacity constraints?
Part 1 - Price and Demand
Sketch and explain the expected relationship between price and quantity demanded.
What This Part Should Cover
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Show a downward-sloping demand curve.
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Explain that higher prices typically reduce quantity demanded.
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Identify intercepts such as maximum demand at very low price and a choke price where demand reaches zero.
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Mention elasticity and segment differences.
Part 2 - Profit as a Function of Price
Sketch total profit as a function of price and explain the shape.
What This Part Should Cover
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Define profit as (p - c) times Q(p) minus fixed cost.
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Explain why profit can be low at very low prices and at very high prices.
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Show the inverted-U shape for linear demand with constant marginal cost.
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Identify the profit-maximizing price where marginal revenue equals marginal cost.
Follow-up Questions
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How would fixed cost affect the profit-maximizing price?
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What if demand has different elasticity by customer segment?
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How would you validate the demand curve before changing price?
