Equilibrium

Market equilibrium (and what a tax does)

The market clears where demand = supply. With linear curves:

\[\text{Demand: } P = A - Q \qquad \text{Supply: } P = C + Q\]

Equilibrium: set them equal → \(Q^* = \dfrac{A-C}{2}\), and \(P^*\) from either curve.
A per-unit tax \(t\) (collected from sellers) drives a wedge: buyers pay \(P_b\), sellers keep \(P_s = P_b - t\). Quantity falls.
Incidence: the side that is less price-sensitive (steeper curve) bears more of the tax. With equally-sloped curves here, buyers and sellers split it evenly.
Deadweight loss (DWL): the tax kills mutually beneficial trades — the little triangle between the curves over the lost quantity.

Try it. Shift demand (A) or supply (C) and watch P*, Q* move. Add a tax to open the wedge and see the deadweight-loss triangle appear.

Demand intercept A: 30 Supply intercept C: 6 Per-unit tax t: 0

Shift demand out (↑A) → both P* and Q* rise. Shift supply out (↓C) → P* falls, Q* rises.
Add a tax → quantity falls, a price wedge opens (buyers pay more, sellers get less), and the shaded deadweight-loss triangle grows with the tax.
With equally-sloped curves, buyers and sellers bear the tax equally — incidence doesn’t depend on who writes the check.