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 €2.00 to €3.00, weekly sales change from 1200 to 960. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €2.00P2 = €3.00Q1 = 1200Q2 = 960
E =
2.Price elasticity of demandHard
The (inverse) demand for a product is P = 30 − 0.2Q, with P in euros. Find the price elasticity of demand E when 45 units are sold.
P = 30 − 0.2QQ = 45
E =
3.Economics conceptsMedium
Both supply and demand for a good increase. What can we say for certain about the new equilibrium?
- AQuantity rises, but the change in price is uncertain
- BBoth price and quantity rise
- CPrice rises, but the change in quantity is uncertain
- DBoth price and quantity fall
4.Economics conceptsHard
Purchasing power parity (PPP) suggests that, in the long run, exchange rates adjust so that:
- AEvery currency ends up having the same nominal value as the US dollar
- BInterest rates are equal in all countries
- CTrade balances are always zero
- DThe same basket of goods costs the same in different countries
3Solutions
1.Price elasticity of demand
Answer: E = −0.5556
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
(960 − 1200)/((1200 + 960)/2) = −240/1080 = −0.2222
Relative change in price
(3 − 2)/((2 + 3)/2) = 1/2.5 = 0.4
Elasticity
E = −0.2222/0.4 = −0.5556
Answer
E = −0.5556
2.Price elasticity of demand
Answer: E = −2.333
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.
Price at this quantity
P = 30 − 0.2·45 = €21.00
Point elasticity
dQ/dP = −1/0.2 = −5
E = −5·21/45 = −2.333
Answer
E = −2.333
|E| > 1: demand is elastic.
3.Economics concepts
Answer: A · Quantity rises, but the change in price is uncertain
Why this is the answer
Both shifts raise quantity, but the demand shift raises price while the supply shift lowers it, so the price effect depends on their relative size.
Answer
A · Quantity rises, but the change in price is uncertain
4.Economics concepts
Answer: D · The same basket of goods costs the same in different countries
Why this is the answer
PPP is based on the law of one price: if a good is cheaper in one country, arbitrage should push exchange rates towards equalising prices, though transport costs and non-traded goods limit this.
Answer
D · The same basket of goods costs the same in different countries
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