Ch 5 Worksheet — Elasticity

Question a

What is the equilibrium price and quantity?

Equilibrium Price ($)

Equilibrium Quantity

Hint Set demand equal to supply: 12 − Q = 2 + 0.5Q. Solve for Q, then plug back in.

Explanation Setting 12 − Q = 2 + 0.5Q gives 10 = 1.5Q, so Q* = 6.67. Plugging back in: P* = 12 − 6.67 = $5.33.

Question b

Calculate the midpoint elasticity of demand when price rises from $4 to $6.

|E_d| (absolute value)

Hint Use the midpoint formula: |E_d| = |(%ΔQ) / (%ΔP)|, where %ΔQ = ΔQ / avg(Q) and %ΔP = ΔP / avg(P).

Explanation At P = $4: Q = 12 − 4 = 8. At P = $6: Q = 12 − 6 = 6.

%ΔQ = (6 − 8) / ((8 + 6)/2) = −2/7 = −0.2857
%ΔP = (6 − 4) / ((4 + 6)/2) = 2/5 = 0.4
|E_d| = 0.2857 / 0.4 = 0.71

Question c

Calculate total revenue at P = $4 and P = $6. Did TR increase or decrease?

TR at $4 ($)

TR at $6 ($)

Hint TR = P × Q. Compare the two values to determine whether demand is elastic or inelastic in this range.

Explanation At P = $4: Q = 8, so TR = 4 × 8 = $32.
At P = $6: Q = 6, so TR = 6 × 6 = $36.

TR rose from $32 to $36 when price increased. This confirms demand is inelastic in this range (|E_d| = 0.71 < 1). When demand is inelastic, a price increase raises total revenue.

Question d

If the cross-price elasticity between organic milk and almond milk is +2.1, are they substitutes or complements? If the income elasticity of organic milk is +1.8, is it a normal or inferior good?

Cross-price type

Income type

Hint Positive cross-price elasticity = substitutes. Positive income elasticity = normal good.

Explanation E_xy = +2.1 > 0 means substitutes (price of almond milk goes up, quantity demanded of organic milk goes up).

E_y = +1.8 > 0 means normal good (income goes up, quantity demanded goes up). Since E_y > 1, it is actually a luxury good.

Question e

If a $2 per-gallon tax is placed on sellers, what is the new equilibrium quantity? (New supply: P = 4 + 0.5Q)

New Equilibrium Quantity

Hint The tax shifts supply up by $2. Set the new supply equal to demand: 12 − Q = 4 + 0.5Q.

Explanation 12 − Q = 4 + 0.5Q gives 8 = 1.5Q, so Q_tax = 5.33.

Compared to Q* = 6.67, 1.33 fewer units are traded. The tax creates a wedge between the price buyers pay and the price sellers receive.

Question 1

Which of the following would make demand for a good MORE elastic?

The good has few substitutes The good is a necessity Consumers have more time to adjust The good represents a tiny fraction of the budget

Hint Think about which factors make consumers more responsive to price changes.

Explanation More time = more elastic. Over time, consumers find alternatives and adjust their behavior. Few substitutes, necessities, and small budget share all make demand less elastic.

Question 2

If |E_d| = 0.5, a 10% price increase causes quantity demanded to:

Fall by 5% Fall by 50% Fall by 20% Rise by 5%

Hint E_d = %ΔQ / %ΔP, so %ΔQ = E_d × %ΔP.

Explanation %ΔQ = 0.5 × 10% = 5%. Since price increased, quantity demanded falls by 5%.

Question 3

When demand is perfectly inelastic, the demand curve is:

Horizontal Vertical Downward-sloping at 45 degrees Upward-sloping

Hint If quantity doesn't change at all when price changes, what shape must the curve be?

Explanation Perfectly inelastic means |E_d| = 0. Quantity doesn't respond to price at all, so the curve is a vertical line. Think of insulin for a diabetic patient.

Question 4

A firm raises its price by 15% and sees total revenue increase by 8%. Demand for this product is:

Elastic Inelastic Unit elastic Perfectly elastic

Hint Use the total revenue test: if price goes up and total revenue also goes up, demand is...

Explanation Price rose and TR rose. This means demand is inelastic. The revenue gained from the higher price outweighs the revenue lost from fewer sales. If demand were elastic, the quantity drop would be so large that TR would fall.

Question 5

Along a linear demand curve, elasticity:

Is constant at all points Varies: elastic at high prices, inelastic at low prices Varies: inelastic at high prices, elastic at low prices Is always unit elastic

Hint On a linear curve, the slope is constant but %ΔQ/%ΔP changes because the base values change.

Explanation At high prices (low Q), a given ΔP is a small percentage of P, but ΔQ is a large percentage of Q, making demand elastic. At low prices (high Q), the opposite is true, making demand inelastic. The midpoint is unit elastic.

Question 6

If the income elasticity of demand for ramen noodles is −0.4, ramen is:

A normal good An inferior good A luxury good A Giffen good

Hint Negative income elasticity means demand falls as income rises.

Explanation E_y < 0 means it's an inferior good. As income rises, people buy less ramen and switch to better food. A Giffen good is a specific type of inferior good where the demand curve slopes upward, which is a different concept.

Question 7

If the price of Coca-Cola rises 10% and the quantity demanded of Pepsi rises 15%, the cross-price elasticity is:

−1.5 +1.5 +0.67 −0.67

Hint E_xy = %ΔQ_d(Pepsi) / %ΔP(Coca-Cola).

Explanation E_xy = +15% / +10% = +1.5. Positive cross-price elasticity means they are substitutes. When Coke's price rises, people switch to Pepsi.

Question 8

A perfectly elastic supply curve is:

Vertical Horizontal Upward-sloping Backward-bending

Hint If suppliers respond infinitely to any price change, the curve is flat.

Explanation Perfectly elastic supply means |E_s| = infinity. Any price change causes an infinite quantity response, so the curve is a horizontal line. At that price, suppliers will provide any quantity the market demands.

Question 9

The midpoint method gives the same elasticity whether you calculate from point A to B or from B to A.

Hint That's exactly why we use the midpoint method instead of the simple percentage method.

Explanation True. The midpoint formula uses the average of the two points as the base, so it gives the same result regardless of direction. The simple percentage method gives different answers depending on which point you start from.

Question 10

If demand is unit elastic, total revenue remains constant when price changes.

Hint Unit elastic means |E_d| = 1, so the % change in Q exactly offsets the % change in P.

Explanation True. When |E_d| = 1, the percentage decrease in quantity exactly offsets the percentage increase in price (and vice versa), so TR = P × Q stays the same.

Question 11

A good with an income elasticity of +0.3 is a luxury.

Hint The cutoff between necessity and luxury is E_y = 1.

Explanation False. E_y = +0.3 means demand rises with income (normal good), but less than proportionally. It is a necessity, not a luxury. A luxury requires E_y > 1.

Question 12

Tax revenue is always higher when demand is more elastic.

Hint Think about what happens to the quantity traded when demand is very elastic.

Explanation False. More elastic demand means a bigger quantity drop from a tax, which means less tax revenue. Governments collect more from taxing inelastic goods (cigarettes, gasoline) because quantity doesn't fall much.

Practice Worksheet

Short Answer — The Organic Milk Market

Multiple Choice

True or False