Microeconomics · Interactive
Elasticity and surplus, worked out
Pick a price on a straight-line demand curve and the diagram shows both numbers a paper actually asks for: the point elasticity there, and the consumer surplus below it, with every step of the working.
P₀ 10.0 · Q₀ 5.0 · CS 50.0
Demand curveConsumer surplusChosen point
The maths, with your numbers
DemandP = a − bQP = 30 − 4.00Q
Price at the chosen pointP₀ = s·a10.0
Quantity at the chosen pointQ₀ = (a − P₀) / b5.0
Point elasticitye = −P₀ / (a − P₀) = −s / (1−s)-0.50
Consumer surplusCS = ½bQ₀²50.0
Reading the diagram
What moves, and why
The demand line is fixed by two numbers
The choke price a is where it meets the price axis, which is the highest price anyone would pay. The slope b is how fast price falls per extra unit sold. Together they fix where the line meets the quantity axis too.
Elasticity only depends on where you are on it
Move the price slider and the elasticity changes even though a and b haven't. Above the midpoint of the line, demand is elastic; below it, inelastic; exactly at the midpoint, it is always unit-elastic, whatever the line's slope or intercept happen to be.
Consumer surplus is the triangle above the price
It is everything buyers would have paid, above what they actually pay, for every unit up to the chosen quantity. It is a triangle whose area is exactly half of base times height, CS = ½bQ₀².
Try it on real questions
From CUET-PG, GATE and IIT JAM
Five questions on exactly this: computing point elasticity and consumer surplus from a demand function.
These are questions from the TestStop bank. A free account answers 10 a day, each with its worked solution; All-Access opens every set with no daily limit.
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