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 €12.00 to €16.00, weekly sales change from 1200 to 560. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €12.00P2 = €16.00Q1 = 1200Q2 = 560
E =
2.Price elasticity of demandHard
The demand for a product is Q = 1500 − 25P, with P in euros. Find the price elasticity of demand E at a price of €18.
Q = 1500 − 25PP = €18
E =
3.Economics conceptsMedium
The law of diminishing marginal returns states that:
- AConsumers get less satisfaction as prices rise
- BTotal output always falls as more workers are hired
- CAdding more of a variable input to a fixed input eventually lowers the extra output per unit added
- DLong-run average costs always fall as output rises
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 = −2.545
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
(560 − 1200)/((1200 + 560)/2) = −640/880 = −0.7273
Relative change in price
(16 − 12)/((12 + 16)/2) = 4/14 = 0.2857
Elasticity
E = −0.7273/0.2857 = −2.545
Answer
E = −2.545
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 = 1500 − 25·18 = 1050
Point elasticity
dQ/dP = −25
E = (dQ/dP)·P/Q = −25·18/1050 = −0.4286
Answer
E = −0.4286
|E| < 1: demand is inelastic.
3.Economics concepts
Answer: C · 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
C · Adding more of a variable input to a fixed input eventually lowers the extra output per unit added
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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