# Harberger's triangle

## Contents

## Definition

**Harberger's triangle** refers to the deadweight loss occurring in the trade of a good or service due to market power of buyers or sellers or a government intervention, that takes the shape of a (curvilinear) triangle in the graph involving the demand curve and supply curve, where two sides of the triangle are usually segments of the demand curve and the supply curve respectively, and the third side is a straight line determined by the nature of market power and the type of government intervention. A Harberger's triangle can be right-pointing (when fewer trades occur than is ideal) or left-pointing (when more trades occur than is ideal).

## Right-pointing Harberger's triangles

These discussions assume that the law of demand and law of supply hold for the particular good.

### Harberger's triangle due to taxes

`Further information: Deadweight loss due to taxation, effect of sales tax on economic surplus`

A sales tax or tariff on the price of a good means that the price for the buyer is greater than the price for the seller. Thus, with such a tax, the equilibrium situation arises at that quantity of goods where the difference between the buyer's and seller's reservation prices equals the value of the sales tax. The Harberger triangle in this case has as one side the vertical line for the quantity of goods traded and the other two sides are the parts of the demand curve and supply curve from that quantity to the equilibrium quantity. The triangle is *rightward-pointing*.

In the figure, the total of the triangular regions E and F is the Harberger triangle representing the welfare loss. The triangle E represents the welfare loss to consumers (the demand side) and the triangle F represents the welfare loss to producers (the supply side).

Note that the areas B and C also represent welfare losses for producers and consumers respectively, but these losses are captured by the taxing authority, hence these do not represent global welfare losses.

### Harberger's triangle due to market power of sellers

`Further information: Deadweight loss due to market power of sellers`

When some sellers have market power, but at the same time lack the ability to perfectly price-discriminate, deadweight losses occur. These deadweight losses can be approximately modeled using a diagram similar to that for sales taxes. Note that unlike the case of taxes, there is no redistribution to the government, but rather, the region that would have been marked as government surplus goes entirely to the seller.

### Harberger's triangle due to price ceiling

`Further information: Effect of price ceiling on economic surplus`

In the case of a binding price ceiling, assuming perfect sorting *and* no additional costs of non-price competition, the deadweight loss is given by the Harberger's triangle. The vertical line is the quantity of goods point on the supply curve for the binding price ceiling, and the other two sides are the parts of the demand curve and supply curve from that quantity to the equilibrium quantity. The triangle is rightward-pointing.

Note that the area of the Harberger's triangle provides a *lower bound* on the deadweight loss in a binding price ceiling situation. The deadweight loss in practice could be higher for two reasons: imperfect sorting among buyers, and the cost of non-price competition.

## Left-pointing Harberger's triangles

### Harberger's triangle due to subsidies

A subsidy to purchases or transactions means that the price for sellers is less than the price for buyers. The Harberger's triangle in this case has as one side the vertical line for the quantity of goods traded and the other two sides are the parts of the demand curve and supply curve from that quantity to the equilibrium quantity.

### Harberger's triangle due to minimum prices (price floors)

## Quadratic nature of area

The area of Harberger's triangle represents the deadweight loss due to taxation, market power, subsidies, or whatever market distortion occurred. Since this is an area, it grows (roughly) quadratically in its dimensions. In other words, we should expect (roughly) that doubling the tax rate will *quadruple* the deadweight loss, or that tripling the tax rate will multiply the deadweight loss by 9.