A Pigouvian tax graph is a supply-and-demand diagram with a third curve added on top, and reading it comes down to three lines and the gaps between them. The vertical axis shows price or cost in dollars. The horizontal axis shows quantity. The three curves show what buyers are willing to pay, what producers spend to make each unit, and what each unit actually costs society once the harm to third parties is counted. Everything else on the graph, including the tax, the deadweight loss, and the revenue, comes out of the space between those lines.
The Three Curves You Are Looking At
The demand curve is labeled Marginal Private Benefit (MPB). It slopes downward because each additional unit is worth slightly less to buyers than the one before it.
The supply curve is labeled Marginal Private Cost (MPC). It captures what the producer actually spends: labor, materials, equipment. It typically slopes upward as output rises.
The third curve is the Marginal Social Cost (MSC). It equals MPC plus the dollar value of harm imposed on people who are not part of the transaction, such as pollution cleanup or public health costs. Because it adds those external damages on top of the producer’s own costs, MSC sits above MPC at every quantity.
The vertical gap between MSC and MPC at any given quantity is the marginal external cost of that unit. That gap is the whole reason the graph exists. If the two cost curves overlapped, there would be no externality to correct.
Market Equilibrium vs. the Social Optimum
With no intervention, the market settles where MPC crosses MPB. Buyers and sellers agree on a price and a quantity that works for them. Neither is paying for the smoke drifting into neighboring lungs or the chemicals seeping into a shared aquifer.
The socially optimal point sits to the left, where MSC crosses MPB. Because the social cost curve runs higher than the private cost curve, that intersection lands at a lower quantity and a higher price. The horizontal distance between the market equilibrium and the social optimum is the overproduction. Every unit produced in that stretch costs society more than it benefits the buyer.
How the Tax Shifts the Cost Curve
A Pigouvian tax is set equal to the marginal external cost at the socially optimal output level, not at the market equilibrium. This distinction matters, because the external cost can change with output, and the tax is calibrated to the efficient point rather than the current one.
On the graph, the tax appears as a per-unit charge added to the producer’s cost curve. MPC shifts upward until it aligns with MSC. Once that shift happens, the new cost curve intersects MPB at the social optimum. Price rises, quantity falls, and the market behaves as though producers are paying for the damage they cause. Consumers see the full cost of what they buy, and they buy less of it.
The Deadweight Loss Triangle
Before the tax, every unit produced between the social optimum and the market equilibrium creates a net loss. For each of those units, MSC exceeds MPB, so the cost to the public outweighs the value to the buyer. On the graph, this net loss forms a triangle bounded by the MSC curve above, the MPB curve below, and vertical lines at the two quantities. Economists call it the deadweight loss, sometimes labeled the Harberger triangle.
Once the tax drops production to the social optimum, the triangle disappears. No more units are being produced in the range where costs exceed benefits. That elimination is the primary welfare gain from the tax, and the triangle’s disappearance is the graphical proof that the policy makes society better off in net terms.
The Revenue Rectangle
Government revenue from the tax appears as a rectangle. Its height equals the per-unit tax, which is the vertical distance between the old MPC and the shifted cost curve. Its width equals the number of units still produced under the tax. Height times width gives total revenue.
Consider the federal gasoline excise tax, which is 18.3 cents per gallon plus a 0.1-cent-per-gallon fee for the Leaking Underground Storage Tank Trust Fund, totaling 18.4 cents per gallon.1Office of the Law Revision Counsel. 26 USC 4081 – Imposition of Tax With billions of gallons consumed annually, the rectangle is short but very wide, and the revenue is substantial.2U.S. Energy Information Administration. How Much Tax Do We Pay on a Gallon of Gasoline and on a Gallon of Diesel Fuel
One warning about reading the rectangle: revenue is not welfare. The welfare gain is the disappearance of the deadweight loss triangle. The rectangle is a transfer from buyers and sellers to the government, and whether that transfer improves the overall picture depends on what the money is spent on, which is a question the graph does not answer.
Reading the Graph in Reverse: Positive Externalities
When an activity generates benefits that spill over to people who did not pay for it, the graph flips. The extra curve is now a Marginal Social Benefit (MSB) sitting above MPB, and the gap represents value enjoyed by third parties. The unregulated market produces too little, and the social optimum, where MSB crosses MPC, sits to the right of the market equilibrium.
A Pigouvian subsidy closes that gap by lowering the effective price to consumers or raising the effective payment to producers, shifting the relevant curve until the market quantity reaches the social optimum. The federal clean vehicle credit works this way, offering up to $7,500 (split into $3,750 for meeting critical mineral requirements and $3,750 for battery component requirements) to buyers of qualifying electric vehicles.3Office of the Law Revision Counsel. 26 US Code 30D – Clean Vehicle Credit The mechanics on the graph mirror the tax case, but every direction is reversed.
Why the Graph Is Cleaner Than the Policy
On paper, the procedure looks simple. Find the MSC curve, measure the gap at the optimum, set the tax at that height. In practice, that gap is one of the hardest numbers in economics to pin down.
Carbon emissions are the clearest example. The Environmental Protection Agency updated its central estimate of the social cost of carbon in 2023 to roughly $190 per metric ton of CO₂. Congressional Budget Office analyses, meanwhile, have modeled carbon taxes starting at just $15 to $25 per metric ton, growing annually by 2 to 8 percent plus inflation.4Congressional Budget Office. Impose a Tax on Emissions of Greenhouse Gases The distance between $190 and $25 is not a rounding error. It reflects real disagreement about discount rates, projected damages, and political feasibility. On the graph, that disagreement means the shifted cost curve could land in very different places, each producing a different equilibrium quantity.
The same measurement problem shows up almost everywhere. Health costs from secondhand smoke depend on exposure patterns, population density, and health care pricing. Runoff damage from a chemical plant depends on soil type, proximity to waterways, and downstream water use. The MSC curve in a textbook is drawn as a smooth, known line. In the real world it is an estimate wrapped in uncertainty.
There is also a circularity worth noticing. The optimal tax equals the marginal external cost at the efficient output level, but the efficient output level is itself defined by the MSC curve the regulator is trying to estimate. Set the tax too low and overproduction persists. Set it too high and a new deadweight loss opens on the other side of the optimum, where units that would have benefited society more than they cost no longer get produced. The graph is a clean picture of a messy problem, and reading it well means keeping both facts in view at once.