Price elasticity of demand
- Price elasticity (midpoint)
- E = (ΔQ/Q̄)/(ΔP/P̄)
- Elastic / inelastic
- |E| > 1 elastic, |E| < 1 inelastic
- Revenue
- TR = P·Q
Microeconomics: cram pack
Formula sheets, the key method steps for every topic and 4 practice problems, with full solutions at the back.
1Formulas and methods
2Practice problems
1.Price elasticity of demandMedium
When the price of a ticket changes from €25.00 to €35.00, weekly sales change from 100 to 80. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €25.00P2 = €35.00Q1 = 100Q2 = 80
E =
2.Price elasticity of demandHard
The demand for a product is Q = 400 − 10P, with P in euros. At which price P is total revenue as large as possible?
Q = 400 − 10P
P = €
3.Economics conceptsMedium
In the long run in monopolistic competition, firms typically:
- AProduce at the minimum of average total cost
- BEarn large economic profits protected by entry barriers
- CCharge a price equal to marginal cost
- DEarn zero economic profit and have excess capacity
4.Economics conceptsHard
Ricardian equivalence suggests that a debt-financed tax cut will:
- AHave little effect on spending, because households save to pay expected future taxes
- BReduce interest rates sharply
- CAlways cause inflation
- DStrongly increase consumption, because households spend most of the tax cut through the multiplier
3Solutions
1.Price elasticity of demand
Answer: E = −0.6667
Price elasticity of demand measures how strongly the quantity demanded reacts to price: E = (% change in quantity)/(% change in price). It is negative for normal goods. |E| > 1 is elastic (revenue falls when price rises), |E| < 1 is inelastic.
Relative change in quantity
(80 − 100)/((100 + 80)/2) = −20/90 = −0.2222
Relative change in price
(35 − 25)/((25 + 35)/2) = 10/30 = 0.3333
Elasticity
E = −0.2222/0.3333 = −0.6667
Answer
E = −0.6667
2.Price elasticity of demand
Answer: P = 20 €
Price elasticity of demand measures how strongly the quantity demanded reacts to price: E = (% change in quantity)/(% change in price). It is negative for normal goods. |E| > 1 is elastic (revenue falls when price rises), |E| < 1 is inelastic.
Revenue as a function of price
R = P·(400 − 10P) = 400P − 10P²
Set the derivative to zero
dR/dP = 400 − 20P = 0
P = 400/20 = €20.00
Answer
P = €20.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: D · Earn zero economic profit and have excess capacity
Why this is the answer
Entry removes profits, but because each firm faces a downward-sloping demand curve, the tangency is to the left of minimum ATC, leaving excess capacity.
Answer
D · Earn zero economic profit and have excess capacity
4.Economics concepts
Answer: A · Have little effect on spending, because households save to pay expected future taxes
Why this is the answer
If consumers are forward-looking and see that government borrowing means higher taxes later, they save the tax cut, so aggregate demand barely changes.
Answer
A · Have little effect on spending, because households save to pay expected future taxes
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