The last chapter, and it uses every one of the others: a wedge on the Chapter 4 diagram, surplus from Chapter 6, elasticity from Chapter 5 deciding the split, and incentives from Chapter 1 explaining why the quantity falls at all.
Before a tax there is one price. After a per-unit tax there are two, separated by exactly the tax — and the single most counter-intuitive result in the course falls straight out of that.
Who the law makes write the cheque is irrelevant to who actually bears the burden. Levy the tax on sellers or on buyers and you get the identical quantity, the identical buyer price and the identical seller price. The legal side is called statutory incidence; the side whose surplus actually falls is economic incidence, and only the second is economics. You can verify this below by flipping a switch.
This is Chapter 1's incentives foundation in its sharpest form: the tax changes costs and benefits, people respond, and the final resting place of the burden is decided by behaviour — not by statute.
One rule carries the whole chapter: the less elastic side bears more of the tax.
Elasticity measures your ability to walk away. The side that can easily switch — to substitutes, to other markets, to not trading at all — walks away from the tax, and the side that is stuck absorbs it. Cigarettes are taxed heavily and buyers pay nearly all of it, because demand is close to inelastic. The same tax on a good with many substitutes lands mostly on sellers.
Set the tax, then make one side steeper and watch the burden move onto it.
A tax raises money and destroys surplus. The two do not scale together, and that asymmetry is the policy point of the chapter.
Doubling a tax rate roughly quadruples the damage while much less than doubling the revenue. It is the standard argument for broad, low taxes over narrow, high ones — and the reason the last few dollars of revenue are the most expensive to collect.
Four shapes, plus the subsidy case, which is a tax with the sign flipped.
| Asked as | Do this | Trap |
|---|---|---|
| "Who bears more of the tax?" | Whichever side is less elastic. | Answering "whoever the law taxes." Statutory incidence is irrelevant. |
| "Calculate the burden per unit" | Buyer burden = Pbuyer − P*. Seller burden = P* − Pseller. They sum to the tax. | Comparing against the new price instead of the original equilibrium. |
| "Find government revenue" | Tax × the new quantity. | Using the old quantity, which overstates it — the tax itself shrank the market. |
| "Find the deadweight loss" | ½ × tax × (Q* − Qnew). | Counting the revenue as a loss. Revenue is a transfer to the government. |
A per-unit subsidy drives the wedge the other way: sellers receive more than buyers pay, quantity rises above the efficient level, and there is still a deadweight loss — because units are now produced whose cost exceeds their value. The benefit also lands mostly on the less elastic side, by exactly the same logic.
Taxes, price controls and trade barriers all do the same two things: they move surplus between groups, and they destroy some of it by preventing trades that were worth making. Keeping those two apart — transfer versus loss — is most of what Chapters 6 and 7 are testing.
Shuffled, and the last of the course. Several items reach back into Chapters 4–6.
| Model | Genuinely computed | Simplified |
|---|---|---|
| The wedge | The post-tax equilibrium by re-solving the shifted system, both prices, each side's burden against the original equilibrium, and the split. The buyer-levied case is solved separately and lands on the same numbers — that identity is computed, not asserted. | Linear curves, a per-unit (not ad valorem) tax, and perfect compliance. |
| Revenue & damage | Quantity, revenue, deadweight loss and remaining surplus at every tax rate; the revenue-maximising tax found by scanning. | No behavioural responses beyond this market — no smuggling, no cross-border shopping, no evasion. |