Areas produce revenue, surplus, and deadweight loss

Match height with the correct post-change quantity.

TR=P× Q. Tax revenue is tax per unit times after-tax quantity. A rectangular profit area is (P-ATC)Q. Triangle area is 1/2 bh for linear consumer surplus, producer surplus, or deadweight loss. The tax wedge or external-cost gap is typically height. The reduction or distortion in quantity is base.

Estimate sign and scale first

If price falls 10 percent and quantity rises 30 percent, demand is elastic before you divide. If an extra unit raises total cost by $12, MC cannot be $120. Direction and rough size are powerful error checks.

Areas on economic graphs multiply a vertical value per unit by a horizontal number of units. Price is dollars per unit and quantity is units, so their rectangle is dollars. The same dimensional logic explains revenue, expenditure, tax revenue, profit rectangles, and surplus triangles. Label axes before calculating. Otherwise a visually correct shape can represent the wrong concept.

Consumer surplus is the area below demand and above the price paid. Producer surplus is above supply and below the price received. For straight lines and a single equilibrium, each may be triangular, but irregular or step-shaped curves require adding the actual geometric regions. Producer surplus is not always profit because fixed cost is not represented by a standard supply curve.

Separate four tax regions

Before tax, 100 units trade at $20. A $4 tax reduces sales to 80. Buyers pay $22 and sellers receive $18. The wedge is $4, tax revenue is 4(80)=$320, and the basic linear deadweight loss is 1/2(4)(20)=$40. Buyers’ price rise is $2 and sellers’ received-price fall is $2, so the burden is split equally in this example.

For a competitive firm’s profit, height is P-ATC at the chosen output and width is quantity. If price is below ATC, the same rectangle represents a loss magnitude. Do not use AVC for profit. AVC answers the shutdown question. A firm can have positive producer surplus while economic profit is negative because revenue covers variable cost and part, but not all, of fixed cost.

Deadweight loss measures gains from trade that disappear, not every dollar transferred. A tax transfers revenue to government. Monopoly transfers some surplus to the producer. A binding price control may transfer surplus between buyers and sellers. DWL arises from trades not made or inefficient trades made. On a tax graph, its base is the reduction in quantity, not the remaining after-tax quantity.

Externality diagrams require social curves. The welfare loss from overproduction lies between marginal social cost and marginal social benefit over the excessive units. Using private supply as the upper boundary would erase the very damage being measured.

Before accepting an area, say its unit and boundaries aloud: “dollars per unit times units,” “between demand and price,” “from efficient quantity to distorted quantity.” This short verbal check distinguishes a meaningful welfare calculation from memorized triangle hunting.

Closed-book formula sprint

Cover this chapter and rebuild, from meaning, the formulas for a marginal value, an average value, midpoint elasticity, total revenue, economic profit, marginal revenue product, tax revenue, and a deadweight-loss triangle. Beside each formula, write its unit and one condition that makes it valid. A symbol recalled without its question, unit, and condition is not yet mastered.