Source: APEC 3002, Applied Microeconomics: Managerial Economics, University of Minnesota Twin Cities
Difficulty: Intermediate | Prerequisites: Companion notes on Regression Analysis and Hypothesis Testing (APEC 3002 Lab 3, Part 2). Basic demand curve concepts from introductory microeconomics.
This is the payoff of the regression work done in Part 2 of the lab. Once you have an estimated demand equation, you can use it to draw demand curves, shift them with advertising, and compute price elasticity at specific points. This is where econometrics meets the managerial question: how sensitive are your customers to price changes, and does advertising make them less sensitive?
If you are comfortable with the regression equation S = 284.81 + 0.5497A − 1.2716P, this section shows you what to do with it.
Using the regression equation from Part 2, demand curves are plotted at three advertising levels (600, 900, 1200). Higher advertising shifts the demand curve to the right (more sales at every price). Price elasticity is inelastic (absolute value below 1) at every tested combination, meaning a 1% price increase reduces quantity demanded by less than 1%. More advertising makes demand even more inelastic.
Demand curve
A graph showing the relationship between the price of a good and the quantity demanded, holding other factors constant. In this lab, each demand curve holds advertising fixed at a particular level.
Shift in demand
A movement of the entire demand curve to the left or right, caused by a change in a non-price factor (here, advertising expenditure). Think of it as the whole curve sliding: at every price, quantity demanded is different.
Price elasticity of demand (Ed)
A measure of how responsive quantity demanded is to a change in price. Formally, it is the percentage change in quantity demanded divided by the percentage change in price. A value between 0 and −1 (in absolute terms, less than 1) means demand is inelastic.
Inelastic demand
Demand where the absolute value of price elasticity is less than 1. Consumers are relatively unresponsive to price changes. In simple terms, raising the price does not drive away many buyers.
Elastic demand
Demand where the absolute value of price elasticity is greater than 1. Consumers are highly responsive to price changes. A small price increase causes a large drop in quantity demanded.
Point elasticity
Elasticity calculated at a specific point on the demand curve (a specific price and quantity), rather than over an arc. This lab uses point elasticity, computed as (dS/dP) × (P/S), where dS/dP is the price coefficient from the regression.
The estimated regression equation is S = 284.81 + 0.5497A − 1.2716P.
To draw a demand curve, fix A at a chosen level and vary P. This gives you a straight line (because the model is linear in P).
Three advertising levels were used: A = 600, A = 900, and A = 1200.
At A = 600: S = 284.81 + 0.5497(600) − 1.2716P = 614.63 − 1.2716P
At A = 900: S = 284.81 + 0.5497(900) − 1.2716P = 779.54 − 1.2716P
At A = 1200: S = 284.81 + 0.5497(1200) − 1.2716P = 944.45 − 1.2716P
The slope of each demand curve (−1.2716) is identical; only the intercept changes. Higher advertising shifts the demand curve rightward (parallel shift), meaning more units are sold at every price.
The graph plots Price on the vertical axis and Quantity Demanded on the horizontal axis.
Three downward-sloping lines appear, one for each advertising level.
The rightmost line (A = 1200) shows the highest sales at any given price.
The leftmost line (A = 600) shows the lowest.
All three have the same slope, confirming the parallel shift.
Point elasticity is calculated using the regression coefficient on price and the specific (P, S) combination:
Price | Advertising | Sales | Price Elasticity |
|---|---|---|---|
$90 | $900 | 665.08 | −0.172 |
$110 | $900 | 639.65 | −0.219 |
$130 | $900 | 614.21 | −0.269 |
$110 | $600 | 474.74 | −0.295 |
$110 | $1200 | 804.55 | −0.174 |
Every elasticity value has an absolute value below 1. The good is inelastic at all tested price and advertising combinations. A 1% increase in price leads to less than a 1% decrease in sales.
As price rises (rows 1 to 3, holding A = 900), elasticity becomes more negative. The good gets slightly more elastic at higher prices, which is a standard result: as you move up a linear demand curve, elasticity increases in absolute value.
As advertising increases (rows 4 and 5, holding P = 110), elasticity decreases in absolute value. More advertising makes consumers less price-sensitive. At A = 600, elasticity is −0.295; at A = 1200, it falls to −0.174. This is the managerial insight: advertising not only boosts sales, it also insulates the firm from the effects of price increases.
E_d = \frac{dS}{dP} \times \frac{P}{S}Where dS/dP is the coefficient on price from the regression (−1.2716), P is the current price, and S is the predicted sales at that price and advertising level.
Example: at P = 110, A = 900, S = 639.65:
E_d = (-1.2716) \times \frac{110}{639.65} = -0.2187Demand curve equation (general form, for a given advertising level A₀):
S = (284.81 + 0.5497 A_0) - 1.2716PThis is a linear demand curve with intercept (284.81 + 0.5497A₀) and slope −1.2716.
Brands use exactly this kind of analysis to set pricing strategy. If demand is inelastic, a firm can raise prices without losing many customers, which increases revenue. Knowing that advertising makes demand more inelastic tells a marketing team that heavy ad spend gives pricing power: the firm can charge more without the usual sales drop.
This is why consumer goods companies (think soft drinks, snack foods) invest heavily in brand advertising. The advertising does not just shift the demand curve right; it also steepens the consumer's attachment to the product, reducing their willingness to switch on price.
"Inelastic means consumers do not care about price at all." They do respond to price, just less than proportionally. A 10% price increase still reduces quantity demanded; it just reduces it by less than 10%.
"The slope of the demand curve is the same as elasticity." The slope (dS/dP = −1.2716) is constant along a linear demand curve, but elasticity changes at every point because P/S changes. Higher prices and lower quantities give higher absolute elasticity.
"Advertising makes the demand curve steeper." In this linear model, advertising shifts the curve rightward but does not change its slope. The slope is always −1.2716. Elasticity changes because the ratio P/S changes, not because the slope does.
"A negative elasticity means something is wrong." Price elasticity of demand is almost always negative (price up, quantity down). What matters is the absolute value. Below 1 = inelastic; above 1 = elastic.
⚠️ Be ready to compute point elasticity from a regression equation. You need the price coefficient, the price, and the predicted sales. Plug and divide.
⚠️ Know why elasticity varies along a linear demand curve even though the slope is constant. This is a classic exam question.
⚠️ Understand the difference between a movement along a demand curve (price change) and a shift of the curve (advertising change). Advertising changes the intercept, not the slope.
⚠️ Be able to explain the managerial implication: advertising reduces price sensitivity (makes demand more inelastic), giving the firm more pricing power.
⚠️ If asked to "draw demand curves at different advertising levels," they are parallel lines with the same slope but different intercepts.
True or False: A parallel rightward shift of the demand curve means the slope has changed.
False. The slope stays the same; only the intercept increases.
Fill in the blank: If |Ed| < 1, demand is ____.
Inelastic.
True or False: On a linear demand curve, elasticity is the same at every point.
False. Elasticity changes because P/S changes even though the slope is constant.
Fill in the blank: When advertising increases from 600 to 1200 (at P = 110), elasticity moves from −0.295 to ____, indicating demand becomes ____ inelastic.
−0.174; more.
True or False: A firm facing inelastic demand can raise price and increase total revenue.
True. The percentage drop in quantity is smaller than the percentage increase in price.
Q: Using S = 284.81 + 0.5497A − 1.2716P, calculate the predicted sales when A = 1200 and P = 110.
A: S = 284.81 + 0.5497(1200) − 1.2716(110) = 284.81 + 659.64 − 139.88 = 804.57 (the lab reports 804.55, with minor rounding differences).
Q: Calculate the point price elasticity of demand at A = 1200, P = 110, S = 804.55.
A: Ed = (−1.2716) × (110 / 804.55) = −0.174. Demand is inelastic.
Q: Why does increasing advertising reduce the absolute value of price elasticity in this model?
A: Higher advertising raises S (the denominator in P/S) without changing the slope dS/dP. Since elasticity = (dS/dP) × (P/S), a larger S makes the ratio P/S smaller, pulling elasticity closer to zero.
Q: At A = 900, how does elasticity change as price rises from $90 to $130?
A: Elasticity goes from −0.172 (at P = 90) to −0.269 (at P = 130). In absolute terms, it increases. As price rises, P/S increases (P goes up, S goes down), so elasticity becomes larger in absolute value. The good moves toward (but does not reach) elastic territory.
Q: A manager wants to raise prices. Should they increase or decrease advertising spending first, based on this analysis?
A: Increase advertising. Higher advertising makes demand more inelastic (lower |Ed|), meaning consumers become less sensitive to price. Raising prices after increasing ad spend will result in a smaller loss of sales than raising prices alone.
This material builds directly on the regression analysis and hypothesis testing covered in the companion study notes (Part 2 of this lab). The regression equation is the foundation for everything here.
It connects forward to optimal pricing and revenue maximisation. If you know the elasticity at different points, you can identify the price that maximises total revenue (which occurs where |Ed| = 1 on a linear demand curve).
The concept of advertising as a demand shifter links to broader topics in marketing economics and industrial organisation, where firms compete on both price and non-price dimensions.
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