Advanced Managerial Economics

A price change becomes a revenue decision the moment you can predict how quantity demanded will respond. If you know that response - especially whether demand is “easy” or “hard” to move - you can forecast the revenue impact of discounts, taxes, and pricing policies without guessing. That’s exactly what demand models and price elasticity are for.

In this chapter you’ll build a workable demand model from a small set of demand data, then use price elasticity to predict what happens to revenue when price changes. You’ll also connect elasticity to policy: when a government adds a per-unit tax, who really bears the cost depends on elasticities. Earlier chapters helped you think about objectives and constraints; now you’ll add a decision-relevant bridge from “price and quantity” to “revenue and impact.”

Learning Objectives

• Build a simple demand model from observed price - quantity pairs and use it to predict outcomes.
• Compute and interpret price elasticity to predict the direction and magnitude of revenue changes.
• Use elasticity intuition to reason about policy impacts like per-unit taxes and price controls.

Building Demand Models from Price - Quantity Data

A demand model is an equation (or rule) that links the price of a product to the quantity consumers are willing to buy. In managerial economics, you rarely get a perfect “true” model, but you often get a good enough approximation over a relevant range of prices.

A starting point is the demand curve, which shows the relationship between price and quantity demanded, holding other factors constant (income, tastes, substitutes, etc.). For most normal goods, the demand curve slopes downward: as price rises, quantity demanded falls.

To build a model you need two ingredients:

1. A functional form: how you relate price to quantity (linear, log-linear, constant elasticity, etc.).

2. Parameter estimates: the numbers that make the model fit your data.

For MBA coursework, the most common “first model” is the linear demand model, written in plain language as:

• Quantity demanded changes at a constant rate as price changes.

So you can treat demand as: “quantity equals a starting level minus a slope times price,” where the slope tells you how sensitive quantity is to price.

A concrete example of “model building”

Suppose a gym sells monthly memberships and tracks sales across a few price points. You might observe:

• At price 40, quantity demanded is 120 memberships/month
• At price 50, quantity demanded is 100 memberships/month

From just two points, you can infer a linear relationship between price and quantity. The slope is the change in quantity divided by the change in price.

Here’s the key learning: the slope is not just math - it’s sensitivity. A steep negative slope means quantity reacts strongly when price changes.

Step-by-step: turning data into a linear demand equation

1. Pick units and keep them consistent. If price is in dollars per month and quantity is memberships per month, keep those exact units.

2. Choose a linear form. Write quantity as Q = a + bP, where b will be negative for a typical demand curve.

3. Use your data to solve for a and b. Two data points are enough for two unknowns.

4. Use the model for predictions. Plug in a new price to forecast quantity.

5. Check plausibility. If the model predicts negative quantity at some price, that’s a sign the linear form isn’t valid outside the observed range.

Practical takeaway prompt

Ask yourself: “If my model slope is -2, what does that mean in human terms?” It means quantity changes by about 2 units for every 1 unit increase in price, within the range where the model fits.

Price Elasticity and Revenue: The “Revenue Switch” Logic

A price elasticity of demand measures how responsive quantity demanded is to a change in price. The most used version in managerial decisions is price elasticity:

• Elastic demand: quantity responds a lot to price (elasticity magnitude greater than 1).
• Inelastic demand: quantity responds a little to price (elasticity magnitude less than 1).
• Unit elastic: elasticity magnitude equals 1.

Elasticity is usually reported as a magnitude (a positive number), even though the true relationship between price and quantity is negative. So you can think: “Elasticity of 2” means a 1% price change causes about a 2% change in quantity, in the opposite direction.

Why elasticity matters for revenue

Revenue is R = P × Q. When price changes, revenue depends on which effect dominates:

• Price effect: higher price tends to raise revenue.
• Quantity effect: lower quantity tends to reduce revenue.

Elasticity tells you which effect wins.

A simple rule of thumb (the “revenue switch” logic):

• If demand is elastic (elasticity > 1), raising price tends to reduce revenue because quantity drops a lot....