Difficulty: Intermediate | Prerequisites: linear demand and supply functions, basic algebra, demand analysis notes from earlier in ECON 22.
This is the chapter where supply meets demand and you learn to solve for the price and quantity the market settles on. It builds directly on the demand and supply functions you have already seen and extends them in two directions: what happens when both curves shift at once (comparative statics), and what happens when the government imposes a per-unit tax (taxation and tax incidence). If you are comfortable writing D(p) = a - bp and S(p) = c + dp and solving for an intersection, you are ready. The tax-incidence results are tested heavily and show up in policy discussions well beyond this course.
Equilibrium price is where quantity demanded equals quantity supplied. For linear curves, p* = (a - c) / (d + b). When both curves shift by the same amount, p* stays put but q* changes. A per-unit tax drives a wedge between the buyer's price and the seller's price, and it does not matter which side of the market is legally required to pay it: the economic burden is split according to the relative slopes of supply and demand.
Competitive market
A market with many buyers and many sellers, none of whom can individually influence the price. Everyone is a price-taker.
In simple terms, no single buyer or seller is big enough to move the price on their own.
Equilibrium price (p)*
The price at which quantity demanded equals quantity supplied: D(p*) = S(p*). At this price, there is no pressure for the price to change.
Think of it as the price the market "wants" to land on.
Equilibrium quantity (q)*
The quantity traded at the equilibrium price. Found by plugging p* back into either D(p) or S(p).
Excess demand (shortage)
When price is below p*, consumers want to buy more than firms are willing to supply. The gap creates upward pressure on price.
Excess supply (surplus)
When price is above p*, firms want to sell more than consumers are willing to buy. The gap creates downward pressure on price.
Comparative statics
The method of comparing one equilibrium to another after a parameter changes (a shift in demand, supply, or both). You are comparing two "static" snapshots, not tracking the transition between them.
In simple terms, you solve the model twice, once before and once after the change, and compare.
Quantity tax (per-unit tax)
A fixed monetary amount charged on every unit sold, such as 10 cents per soda. Denoted t.
Demand price (PD)
The price the buyer pays, inclusive of any tax.
Supply price (PS)
The price the seller receives after paying any tax. The relationship is PD = PS + t.
Tax incidence
How the burden of a tax is split between buyers and sellers. Determined by the relative slopes (elasticities) of supply and demand, not by who is legally required to remit the tax.
In simple terms, the side of the market that is less responsive to price changes bears the larger share of the tax.
A competitive market has many buyers and sellers; everyone is a price-taker.
Equilibrium occurs where D(p*) = S(p*).
For linear functions D(p) = a - bp and S(p) = c + dp, set them equal and solve:
a - bp = c + dp
a - c = (d + b)p
p* = (a - c) / (d + b)
Plug p* back into either function to get q*.
Example: D(p) = 120 - 10p, S(p) = 4 + 8p. a = 120, b = 10, c = 4, d = 8. p* = (120 - 4)/(8 + 10) = 116/18 ≈ 6.44. q* = 4 + 8(6.44) ≈ 56.
If price is below p*, there is excess demand: consumers want more than firms will supply at that price. Firms can raise their price and still find buyers, pushing price upward toward p*.
If price is above p*, there is excess supply: firms want to sell more than consumers will buy. Firms must lower their price to attract buyers, pushing price downward toward p*.
p* is the only price at which neither consumers nor producers can improve their position by changing behaviour. That is why it is called an equilibrium: it is stable.
Equilibrium does not mean "good" or "fair." It simply means the market has no internal pressure to move away from that point.
If both D(p) and S(p) shift by the same amount m (both decrease by m, or both increase by m), the equilibrium price does not change.
Proof: D'(p) = D(p) - m and S'(p) = S(p) - m. Setting D'(p) = S'(p) gives D(p) - m = S(p) - m, which simplifies to D(p) = S(p). Same equation, same p*.
However, q* does change. If both curves shift down by m (leftward), q* falls by m. If both shift up by m (rightward), q* rises by m.
Graphically: both curves slide in the same direction by the same distance. They cross at the same height (same p*) but at a different horizontal position (different q*).
A quantity tax t is charged on every unit sold. Example: each soda taxed 10 cents.
PD is the price the buyer pays. PS is the price the seller receives. The relationship is PD = PS + t.
If the seller pays the tax: soda costs the buyer $1 (PD = $1), seller keeps $0.90 (PS = $0.90), tax = $0.10.
If the buyer pays the tax: same outcome in equilibrium.
Whether the tax is levied on the buyer or the seller, the equilibrium condition is the same: D(PD) = S(PS) with PD = PS + t.
Seller-pays framing: D(PS + t) = S(PS).
Buyer-pays framing: D(PD) = S(PD - t). Since PD = PS + t, this is the same equation.
The economic burden is determined by the slopes of supply and demand, not by the legal assignment.
With D(p) = a - bp and S(p) = c + dp and tax t:
Seller's equilibrium price: PS* = (a - c - bt) / (d + b)
Buyer's equilibrium price: PD* = (a - c + dt) / (d + b)
Notice: PS* < p* (sellers get less) and PD* > p* (buyers pay more). The tax is shared.
The -bt term in PS* depends on b (the demand slope). The +dt term in PD* depends on d (the supply slope).
If demand is very steep (small b), buyers bear most of the tax.
If supply is very steep (small d), sellers bear most of the tax.
D(p) = 100 - 38p, S(p) = -20 + 2p. So a = 100, b = 38, c = -20, d = 2.
No-tax equilibrium: p* = (100 - (-20))/(2 + 38) = 120/40 = 3... wait, the notes give p* = (100-20)/(38+2) = 80/40 = 2. Here c = 20 (positive), so S(p) = 20 + 2p per the notes' sign. Correcting: a = 100, b = 38, c = 20, d = 2. p* = (100 - 20)/(2 + 38) = 80/40 = 2. q* = 20 + 2(2) = 24.
With t = 0.1: PS* = (100 - 20 - 38(0.1))/40 = (80 - 3.8)/40 = 76.2/40 ≈ 1.905. PD* = (100 - 20 + 2(0.1))/40 = 80.2/40 ≈ 2.005.
Buyers pay 2.005 - 2 = 0.005 more (5% of the tax). Sellers receive 2 - 1.905 = 0.095 less (95% of the tax).
Why the lopsided split? Demand is very steep (b = 38), so consumers are price-insensitive compared to the flat supply curve (d = 2). Sellers, being the more responsive side, absorb nearly all of the tax.
Equilibrium price (linear supply and demand)
p* = (a - c) / (d + b)
where D(p) = a - bp, S(p) = c + dp.
Equilibrium quantity
q* = D(p*) = S(p*). Plug p* into either function.
Post-tax seller price
PS* = (a - c - bt) / (d + b)
Post-tax buyer price
PD* = (a - c + dt) / (d + b)
Price wedge
PD - PS = t (always). The tax equals the gap between what the buyer pays and what the seller keeps.
The tax-incidence result explains why excise taxes on cigarettes or petrol are largely borne by consumers: demand for these goods is relatively inelastic (people keep buying even when prices rise), while supply is more elastic. Legislators may announce that a tax is on producers, but the economics shows most of the burden passes through to buyers.
Comparative statics is the basic analytical tool behind any headline that reads "what happens to house prices if both supply and demand rise?" If both shift equally, price holds and quantity rises, which matches what you see in a growing city where construction keeps pace with population growth.
Students often think equilibrium means the market is in a "good" or "fair" state. Equilibrium simply means stable: no participant can do better by unilaterally changing behaviour. It says nothing about fairness or welfare.
A frequent error is assuming that whoever is legally required to pay the tax bears the full cost. The legal assignment is irrelevant in equilibrium; the economic burden depends on relative slopes (elasticities).
When both supply and demand shift by the same amount, students sometimes expect both p* and q* to stay the same. Only p* stays the same; q* shifts by m.
Students sometimes confuse the direction of the shift. A decrease in both D and S by m shifts both curves to the left (lower quantity at every price), not downward in the price sense.
⚠️ The equilibrium-price formula p* = (a - c)/(d + b) is used constantly. Be able to identify a, b, c, d from any linear supply and demand pair and solve quickly.
⚠️ Tax-incidence questions are high-value exam material. You will be asked to compute PS* and PD* and explain who bears the larger share and why.
⚠️ The invariance result (it does not matter who legally pays the tax) is a classic true/false or short-answer exam question. Be ready to prove it in two lines.
⚠️ Comparative statics: if a question says "both curves shift by the same amount," the answer is that p* is unchanged and q* changes by that amount. This is a quick-marks question if you spot the pattern.
True or false: At equilibrium, every consumer who wants to buy at p* can find a willing seller. (True.)
If D(p) = 60 - 3p and S(p) = 10 + 2p, what is p*? ((60 - 10)/(2 + 3) = 50/5 = 10.)
Fill in the blank: When a per-unit tax is imposed, the gap between PD and PS always equals ______. (t, the tax per unit.)
True or false: If both demand and supply decrease by 5 units at every price, the equilibrium price falls. (False: p* stays the same; only q* falls.)
True or false: A tax on sellers produces a different equilibrium from a tax on buyers. (False: the equilibrium prices and quantity are the same regardless of legal assignment.)
Q: Given D(p) = 80 - 5p and S(p) = 10 + 3p, find p and q.**
A: p* = (80 - 10)/(3 + 5) = 70/8 = 8.75. q* = 80 - 5(8.75) = 80 - 43.75 = 36.25.
Q: Using the same functions, a tax of t = 2 is imposed. Find PS and PD.**
A: PS* = (80 - 10 - 5(2))/(3 + 5) = (70 - 10)/8 = 60/8 = 7.5. PD* = (80 - 10 + 3(2))/(3 + 5) = (70 + 6)/8 = 76/8 = 9.5. Check: PD* - PS* = 9.5 - 7.5 = 2 = t.
Q: In the example above, what share of the tax do buyers bear?
A: Buyers pay 9.5 - 8.75 = 0.75 more. Sellers receive 8.75 - 7.5 = 1.25 less. Buyers bear 0.75/2 = 37.5%, sellers bear 62.5%. Supply is steeper (d = 3 < b = 5), so sellers bear more.
Q: If D(p) and S(p) both increase by 12, what happens to p and q?**
A: p* is unchanged. q* increases by 12.
The equilibrium framework here is the foundation for welfare analysis: consumer surplus is the area above p* and below the demand curve, producer surplus is the area below p* and above the supply curve. Taxes create a deadweight loss, which you will study next.
Elasticity from the demand-analysis notes feeds directly into tax incidence. The more inelastic side of the market bears the larger share of the tax. This connection is tested frequently.
Comparative statics reappears whenever the course introduces a policy or shock (tariffs, subsidies, price ceilings, price floors) and asks what happens to p* and q*.
market equilibrium, competitive market, price-taker, equilibrium price, equilibrium quantity, supply and demand intersection, excess demand, shortage, excess supply, surplus, comparative statics, demand shift, supply shift, parallel shift, per-unit tax, quantity tax, excise tax, tax incidence, tax burden, demand price, supply price, price wedge, statutory incidence vs economic incidence, deadweight loss, ECON 22, Chapter 16, intermediate microeconomics