Signature
Delta_CS = (P_0 - P_1) * (Q_0 + Q_1) / 2
| Inputs | Definition | Unit |
|---|---|---|
P_0 | Price paid per unit before the change | currency per unit |
P_1 | Price paid per unit after the change | currency per unit |
Q_0 | Units bought at P_0 | units per person per period |
Q_1 | Units bought at P_1 | units per person per period |
Delta_CS | Gain in consumer surplus from the price change, negative for a loss | currency per person per period |
|---|
Function
Welfare change measurement and aggregation function
Converts each person's gain or loss from a change into money, with the compensating or equivalent variation or the consumer surplus approximation, and then ranks the change for society: by adding the money measures, as the Kaldor-Hicks potential compensation test does, or by combining individual outcomes with an explicit social welfare function that states how gains to one person are set against losses to another.
Try this function
Implementations
Excel
Consumer surplus change from two price and quantity points
With the old and new prices in PriceOld and PriceNew and the quantities in QtyOld and QtyNew, Excel returns the change in consumer surplus.
=(PriceOld-PriceNew)*(QtyOld+QtyNew)/2
Assumptions
Straight-line demand between the old and new prices
The demand curve is a straight line between the two observed points. For a curved demand function the trapezoid is an approximation; with the Cobb-Douglas demand of the CV and EV example it gives 150 against the exact area of 138.63.
Small income effects
Consumer surplus approximates CV and EV well when spending on the good is a small share of income and income effects are modest.
Worked examples
Cut in an outpatient charge
A charge falls from 20 to 10 pounds a visit and use rises from 4 to 5 visits a year. Consumer surplus rises by 45 pounds a person a year. The figures are illustrative.
P_0 = 20; P_1 = 10; Q_0 = 4; Q_1 = 5; Delta_CS = 45
Introducing a charge for a free service
Introducing a charge of 10 pounds on a free service reduces use from 5 to 4 visits and consumer surplus by 45 pounds a person a year; the 40 pounds collected is a transfer, and the remaining 5 pounds is the deadweight loss triangle.
P_0 = 0; P_1 = 10; Q_0 = 5; Q_1 = 4; Delta_CS = -45
Common errors
Counting only the saving on the original quantity
Multiplying the 10-pound cut by the original 4 visits gives 40 pounds and misses the 5-pound surplus on the extra visit. For a price rise the same shortcut overstates the loss.
Sources
Consumer surplus as an approximation to exact welfare measures
Mas-Colell A, Whinston MD, Green JR. Microeconomic Theory. New York: Oxford University Press; 1995. Section 3.I: the area variation (Marshallian consumer surplus) lies between the compensating and equivalent variations for a single price change and is exact when income effects are absent.
Canonical Identity
Stable URI · Machine-readable · Resolvable · CC BY 4.0