Supply-Demand Shock Simulator

equilibrium response to market shocks

Worked example — Supply-Demand Shock Simulator

Equilibrium price	33.33
Equilibrium quantity	53.33

These are the values the calculator shows when the page opens. Change any input above to recompute them.

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why slopes matter for shock impact 🖖

The shape of these two lines determines who absorbs a shock, and it is visible directly in the algebra. A pure demand shift moves the new equilibrium along the supply line; a pure supply shift moves it along the demand line. Differentiating P* = (a−c)/(b+d) shows a demand shock's quantity response divided by its price response, ΔQ/ΔP, works out to exactly d — the supply curve's own slope coefficient. A large d means quantity absorbs most of the shock while price barely moves, since supply flexes readily to meet new demand; a small d forces almost all the adjustment onto price instead. That is the algebraic reason inelastic markets like housing or oil see demand shocks slam mostly into price rather than quantity.

reading the crossing point 🖖

Equilibrium is simply where the supply and demand lines cross — the one price at which the quantity people want to buy equals the quantity producers offer. Shift a curve and that crossing slides to a new price and quantity. A rise in demand pushes both price and quantity up, while a rise in supply pushes quantity up but price down.

why raw data hides both curves 🖖

Plot real-world price and quantity points and you recover neither the supply nor the demand curve. Because both shift at once, the scatter traces a blend of the two. Elmer Working spelled this out in 1927 — untangling them needs an instrumental variable that moves only one curve, like weather that shifts supply alone.

Problem solved in full

A tax of 6 per unit on Q = 120 − 2P 6 steps
Demand is Q = 120 − 2P and supply is Q = 20 + P. Find the equilibrium, then put a tax of 6 per unit on the sellers and work out who actually pays it.
1. Two straight lines, one falling and one rising. Equilibrium is where the quantities agree, not where the prices do — price is the variable being solved for.
  
  $Q_{d} = 120 - 2 P, Q_{s} = 20 + P$
2. Set them equal and solve. Both curves must return the same quantity at that price, which is the check.
  
  $120 - 2 P = 20 + P \Rightarrow 3 P = 100 \Rightarrow P^{*} = 33.33, Q^{*} = 20 + 33.33 = 53.33$
3. Elasticity is the slope reweighted by where you are standing. The two slopes differ by a factor of two, and so do the elasticities, because both are evaluated at the same point.
  
  $ε_{d} = \frac{d Q _{d}}{d P} \frac{P}{Q} = - 2 \cdot \frac{33.33}{53.33} = - 1.25, ε_{s} = + 1 \cdot \frac{33.33}{53.33} = 0.625$
4. A tax on sellers means the price they keep is the price paid minus t, so the supply curve shifts up by exactly t. Re-solve — the constant is the only thing that moved.
  
  $Q_{s} = 20 + (P - t) \Rightarrow 3 P = 100 + t; t = 6 : P^{'} = 35.33, Q^{'} = 49.33$
5. Split the 6. The buyer's share is the elasticity of supply over the sum of the two, which is why the inelastic side pays more: it is the side with fewer alternatives.
  
  $buyers + 2.00, sellers - 4.00; buyer share = \frac{ε _{s}}{ε _{s} + ∣ ε _{d} ∣} = \frac{0.625}{1.875} = \frac{1}{3}$
6. The triangle between the curves over the lost quantity is the loss to nobody's benefit, and it grows with the square of the tax — doubling the rate quadruples the waste.
  
  $DWL = \frac{1}{2} t Δ Q = \frac{1}{2} \times 6 \times 4 = 12$
Answer

Buyers pay 2 of the 6 and sellers absorb 4, however the law is written. Legal incidence and economic incidence are different things: the tax is collected from sellers here, and two thirds of it still lands on them, because the split follows elasticity and demand at this equilibrium is twice as elastic as supply. Reverse the statute and charge the buyers instead — the equilibrium quantity, both net prices and the whole outcome are identical. The 12 of deadweight loss is the part nobody gets: four units of trade that were worth more to buyers than to sellers, and now do not happen.

$P^{*} = 33.33, Q^{*} = 53.33; a tax splits \frac{1}{3} buyers, \frac{2}{3} sellers$

References (1)

Insight block 3 — why a scatter of price and quantity recovers neither curve: E. J. Working, "What Do Statistical 'Demand Curves' Show?" The Quarterly Journal of Economics 41(2), 212–235, 1927.

By the 42Math team · Updated 2026-05-29

Reviewed against published sources. Corrections welcome. Editorial policy · Corrections

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Example problems

demand boom - Demand rises by 20: price goes 33.33 to 40.00 and quantity 53.33 to 60.00, so ΔQ/ΔP = 1.0000 - exactly d, the supply slope, as the algebra above says.
supply crisis - Supply falls by 20 and the price lands on 40.00, the same as Demand boom. Quantity does not: it drops 13.33 where the demand shock raised it 6.67. ΔQ/ΔP = -2, which is -b.
dual shock - Both curves move at once and ΔQ/ΔP comes out -0.3333, which is neither d nor -b. That is the identification problem: the ratio you can observe identifies nothing.