Market Equilibrium Lab for a game-theory standoff

Where the downward demand curve crosses the upward supply curve, the market clears: that price and quantity are the equilibrium. Shifting either curve moves it. The shaded triangles are consumer and producer surplus — the total gains from trade. A per-unit tax lifts the supply curve, raising price, cutting quantity, and creating deadweight loss.

Elasticity measures how much quantity demanded responds to price. Where demand is elastic (|E| > 1), a price cut raises total revenue; where it is inelastic, a price cut lowers revenue. On a straight-line demand curve the top half is elastic, the bottom half inelastic, and revenue peaks exactly at the midpoint where elasticity equals one.

At a 0% tax rate the government collects nothing; at 100% no one bothers to earn taxable income, so it also collects nothing. Somewhere between lies a revenue-maximizing rate — the peak of the Laffer curve. How responsive people are to taxes (the elasticity) sets where that peak falls. It is descriptive, not a policy prescription.