Perfectly Inelastic
What is Perfectly Inelastic?
Perfectly inelastic demand is when any change in price leads to no change in quantity demanded.
In perfectly inelastic demand, consumers are completely insensitive to price changes. This means that changes in price have no effect on the quantity demanded. Perfectly inelastic demand is a theoretical concept that is not often observed in real markets.
Perfectly Inelastic: a worked example
A hospital orders 200 doses a month of a drug with no substitute. The supplier raises the price from $40 to $60, a 50 percent increase, and the hospital still orders 200 doses. The percentage change in quantity demanded is 0 ÷ 200 = 0 percent, so price elasticity of demand is 0 ÷ 50 = 0. The supplier's revenue climbs from 200 × $40 = $8,000 to 200 × $60 = $12,000, a gain of $4,000. Revenue rose by exactly the same 50 percent as the price, because quantity absorbed none of the change. Now add a $10 per dose excise tax. The price buyers pay rises the full $10 to $70, quantity stays at 200, and the hospital hands over all 200 × $10 = $2,000 of tax while the seller still nets $60 a dose.
The mistake students make with perfectly inelastic
A zero in the numerator tempts students to flip the formula, dividing the 50 percent price change by the 0 percent quantity change and reporting an undefined or infinite answer. The percentage change in quantity demanded always sits on top, so a quantity that never moves produces a coefficient of exactly zero. The second slip is calling any steep demand curve perfectly inelastic. Steep is merely inelastic. Perfectly inelastic means strictly vertical, with the identical quantity purchased at every single price.
Perfectly Inelastic questions
What does a perfectly inelastic demand curve look like on a graph?
A perfectly inelastic demand curve is a vertical line sitting at one fixed quantity. Buyers purchase that same amount whether the price is high or low, so the curve never leans. With price on the vertical axis and quantity on the horizontal axis, the demand line rises straight up from the single quantity consumers insist on. Any shift in supply then moves price up or down along that line while the quantity traded stays put.
Who bears the tax burden when demand is perfectly inelastic?
Consumers bear the entire burden of a per unit tax when demand is perfectly inelastic. Sellers can pass the full tax into the price because quantity demanded does not fall in response, so the price buyers pay rises by the exact amount of the tax while the price sellers keep is unchanged. Deadweight loss is zero in this case, since no mutually beneficial trades are lost. The mirror image happens when supply is perfectly inelastic and sellers absorb the whole tax.
What is an example of a perfectly inelastic good?
Perfectly inelastic goods are classroom constructions rather than measured cases. The standard illustration is a life saving medicine taken in a dose a doctor fixes, where the patient buys that same quantity whatever the price. A capped number of permits is a different animal, since that vertical line is a supply curve rather than a demand curve. Even genuine necessities bend at extreme prices, because a high enough price eventually forces buyers to ration or go without. Exam questions use the vertical demand curve to demonstrate full tax pass through and zero deadweight loss.
Formula / Example
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Related terms
Common comparisons
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