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 €15.00 to €21.00, weekly sales change from 400 to 300. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €15.00P2 = €21.00Q1 = 400Q2 = 300
E =
2.Price elasticity of demandHard
The (inverse) demand for a product is P = 120 − 1Q, with P in euros. Find the price elasticity of demand E when 48 units are sold.
P = 120 − 1QQ = 48
E =
3.Economics conceptsMedium
A Nash equilibrium is a situation where:
- AThe players agree to cooperate through a binding contract that maximises their combined total payoff
- BOne player has won and the others have lost
- CAll players achieve the highest possible total payoff
- DNo player can improve their payoff by changing strategy alone, given the others' strategies
4.Economics conceptsHard
The "Taylor principle" says that, to stabilise inflation, a central bank should respond to a 1 percentage point rise in inflation by:
- AKeeping the nominal rate unchanged
- BCutting the nominal rate
- CRaising the nominal interest rate by more than 1 percentage point
- DRaising the nominal interest rate, but by less than 1 percentage point
3Solutions
1.Price elasticity of demand
Answer: E = −0.8571
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
(300 − 400)/((400 + 300)/2) = −100/350 = −0.2857
Relative change in price
(21 − 15)/((15 + 21)/2) = 6/18 = 0.3333
Elasticity
E = −0.2857/0.3333 = −0.8571
Answer
E = −0.8571
2.Price elasticity of demand
Answer: E = −1.5
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 = 120 − 1·48 = €72.00
Point elasticity
dQ/dP = −1/1 = −1
E = −1·72/48 = −1.5
Answer
E = −1.5
|E| > 1: demand is elastic.
3.Economics concepts
Answer: D · No player can improve their payoff by changing strategy alone, given the others' strategies
Why this is the answer
In a Nash equilibrium each strategy is a best response to the others; the outcome need not be efficient, as the Prisoner's Dilemma shows.
Answer
D · No player can improve their payoff by changing strategy alone, given the others' strategies
4.Economics concepts
Answer: C · Raising the nominal interest rate by more than 1 percentage point
Why this is the answer
Only by raising nominal rates more than one-for-one does the real interest rate rise, cooling demand and bringing inflation back down.
Answer
C · Raising the nominal interest rate by more than 1 percentage point
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