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 €40.00 to €44.00, weekly sales change from 200 to 160. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €40.00P2 = €44.00Q1 = 200Q2 = 160
E =
2.Price elasticity of demandHard
The demand for a product is Q = 5000 − 50P, with P in euros. At which price P is total revenue as large as possible?
Q = 5000 − 50P
P = €
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
- BConsumers get less satisfaction as prices rise
- CLong-run average costs always fall as output rises
- DTotal output always falls as more workers are hired
4.Economics conceptsHard
The Fisher effect predicts that, in the long run, a permanent 2 percentage point rise in expected inflation will:
- ARaise real interest rates by about 2 points
- BRaise nominal interest rates by about 2 points, leaving real rates unchanged
- CHave no effect on nominal interest rates, so real interest rates fall by about 2 points
- DLower nominal interest rates by about 2 points
3Solutions
1.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.
Relative change in quantity
(160 − 200)/((200 + 160)/2) = −40/180 = −0.2222
Relative change in price
(44 − 40)/((40 + 44)/2) = 4/42 = 0.09524
Elasticity
E = −0.2222/0.09524 = −2.333
Answer
E = −2.333
2.Price elasticity of demand
Answer: P = 50 €
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.
Revenue as a function of price
R = P·(5000 − 50P) = 5000P − 50P²
Set the derivative to zero
dR/dP = 5000 − 100P = 0
P = 5000/100 = €50.00
Answer
P = €50.00
At this price E = −1: demand is unit elastic.
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 · Raise nominal interest rates by about 2 points, leaving real rates unchanged
Why this is the answer
Lenders demand compensation for expected inflation, so nominal rates move one-for-one with it in the long run while the real rate is set by real factors.
Answer
B · Raise nominal interest rates by about 2 points, leaving real rates unchanged
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