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 €8.00 to €8.50, weekly sales change from 200 to 190. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €8.00P2 = €8.50Q1 = 200Q2 = 190
E =
2.Price elasticity of demandHard
The demand for a product is Q = 500 − 10P, with P in euros. Find the price elasticity of demand E at a price of €15.
Q = 500 − 10PP = €15
E =
3.Economics conceptsMedium
A price ceiling set below the equilibrium price typically causes:
- AA surplus
- BNo change in the market
- CA shortage
- DAn increase in supply
4.Economics conceptsHard
The "paradox of thrift" suggests that if all households try to save more during a recession:
- ATotal income may fall, so total saving does not rise
- BInterest rates will rise sharply
- CInvestment and growth will rise immediately
- DInflation will increase
3Solutions
1.Price elasticity of demand
Answer: E = −0.8462
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
(190 − 200)/((200 + 190)/2) = −10/195 = −0.05128
Relative change in price
(8.5 − 8)/((8 + 8.5)/2) = 0.5/8.25 = 0.06061
Elasticity
E = −0.05128/0.06061 = −0.8462
Answer
E = −0.8462
2.Price elasticity of demand
Answer: E = −0.4286
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.
Quantity at this price
Q = 500 − 10·15 = 350
Point elasticity
dQ/dP = −10
E = (dQ/dP)·P/Q = −10·15/350 = −0.4286
Answer
E = −0.4286
|E| < 1: demand is inelastic.
3.Economics concepts
Answer: C · A shortage
Why this is the answer
A binding maximum price raises quantity demanded and lowers quantity supplied, creating excess demand, as with rent control.
Answer
C · A shortage
4.Economics concepts
Answer: A · Total income may fall, so total saving does not rise
Why this is the answer
Higher saving reduces consumption and aggregate demand, lowering income; with lower income, aggregate saving may end up no higher, as Keynes argued.
Answer
A · Total income may fall, so total saving does not rise
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