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 €20.00 to €18.00, weekly sales change from 1000 to 1120. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €20.00P2 = €18.00Q1 = 1000Q2 = 1120
E =
2.Price elasticity of demandHard
The demand for a product is Q = 40 − 2P, with P in euros. Find the price elasticity of demand E at a price of €6.
Q = 40 − 2PP = €6
E =
3.Economics conceptsMedium
The law of diminishing marginal returns states that:
- AAdding more of a variable input to a fixed input eventually lowers the extra output per unit added
- BLong-run average costs always fall as output rises
- CTotal output always falls as more workers are hired
- DConsumers get less satisfaction as prices rise
4.Economics conceptsHard
The Laffer curve illustrates that:
- ATax revenue is unrelated to tax rates
- BBeyond some point, raising tax rates can reduce total tax revenue
- CHigher tax rates always increase tax revenue
- DLower tax rates always reduce tax revenue, whatever the starting rate
3Solutions
1.Price elasticity of demand
Answer: E = −1.075
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
(1120 − 1000)/((1000 + 1120)/2) = 120/1060 = 0.1132
Relative change in price
(18 − 20)/((20 + 18)/2) = −2/19 = −0.1053
Elasticity
E = 0.1132/−0.1053 = −1.075
Answer
E = −1.075
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 = 40 − 2·6 = 28
Point elasticity
dQ/dP = −2
E = (dQ/dP)·P/Q = −2·6/28 = −0.4286
Answer
E = −0.4286
|E| < 1: demand is inelastic.
3.Economics concepts
Answer: A · Adding more of a variable input to a fixed input eventually lowers the extra output per unit added
Why this is the answer
In the short run, with at least one fixed factor, marginal product eventually falls, which makes marginal cost rise.
Answer
A · Adding more of a variable input to a fixed input eventually lowers the extra output per unit added
4.Economics concepts
Answer: B · Beyond some point, raising tax rates can reduce total tax revenue
Why this is the answer
Very high rates discourage taxed activity or encourage avoidance, so revenue peaks at some rate between 0 and 100%; where that peak lies is debated.
Answer
B · Beyond some point, raising tax rates can reduce total tax revenue
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