Chapter 5 — Market Equilibrium

Fig 1 — Educational Diagram: Meaning and Definition of Market Equilibrium

Meaning: Market equilibrium is a state in a competitive market where the quantity demanded of a good equals the quantity supplied. At this point the market 'clears' — there is neither a shortage nor a surplus — and the price at which this happens is called the equilibrium price (market-clearing price); the corresponding quantity is the equilibrium quantity.

Formal definition: Market equilibrium occurs at a price P* and quantity Q* such that Qd(P*) = Qs(P*), where Qd(P) is the demand function and Qs(P) is the supply function.

How equilibrium is achieved (price-adjustment mechanism):

• If price is below P* (P < P*), quantity demanded exceeds quantity supplied (Qd > Qs) — this is excess demand (shortage). Sellers raise prices to capture higher willingness to pay; the price rises until the shortage disappears.
• If price is above P* (P > P*), quantity supplied exceeds quantity demanded (Qs > Qd) — this is excess supply (surplus). Sellers lower prices to sell inventories; the price falls until the surplus disappears.
• Through these adjustments, a competitive market tends toward the stable equilibrium where Qd = Qs.

Determinants that affect the equilibrium: Anything that shifts demand or supply curves will change P* and/or Q*. Examples: income, tastes, prices of related goods, number of buyers (shift demand); input costs, technology, number of sellers (shift supply).

Comparative statics: When demand or supply shifts, the new equilibrium is found by equating the new demand/supply. For a rightward shift in demand (higher demand at each price), both equilibrium price and quantity typically rise. For a rightward shift in supply, equilibrium quantity rises and price falls.

Stability: In the basic competitive model with price adjustments responding to excess demand or supply, equilibrium is stable: deviations trigger movements of price back toward P*.

Limitations & notes: Real markets may not instantly clear because of price rigidities (wages, contracts), government controls (price ceilings/floors), imperfect competition, externalities, or information problems. In such cases shortages or surpluses can persist.

Fig 2 — Educational Diagram: Demand and Supply Schedules and Curves

Basic definitions

Demand schedule is a table that shows the quantities of a good that consumers are willing and able to buy at different prices, ceteris paribus. It illustrates the law of demand: when price rises, quantity demanded falls, and vice versa.

Supply schedule is a table that shows the quantities of a good that producers are willing and able to sell at different prices, ceteris paribus. It illustrates the law of supply: when price rises, quantity supplied rises, and vice versa.

From schedules to curves

When the price–quantity pairs from a schedule are plotted with price on the vertical axis (Y) and quantity on the horizontal axis (X) and connected, we get the demand curve (typically downward sloping) and the supply curve (typically upward sloping). Curves represent continuous relationships; schedules are discrete tables.

Interpretation and slopes

• Demand curve slope is negative: higher P → lower Qd.
• Supply curve slope is positive: higher P → higher Qs.
• Slope (linear) = change in P / change in Q. For linear demand Qd = a − bP, slope = −1/b in P–Q graph (but often we refer to coefficient b as the responsiveness).

Movements along vs shifts

• Movement along a curve: change in quantity demanded (or supplied) due to a change in the price of the good itself (point moves on same curve).
• Shift of the entire curve: change in demand (or supply) due to non-price determinants.

Non-price determinants that shift curves

• Demand shifts: consumer income, tastes and preferences, prices of related goods (substitutes and complements), expectations, number of buyers.
• Supply shifts: input prices, technology, taxes/subsidies, expectations, number of sellers, natural conditions.

Connection to market equilibrium

The equilibrium price and quantity are found where the demand and supply curves intersect. At equilibrium, quantity demanded equals quantity supplied.

Graphing tips

• Label axes: Price (P) on vertical axis, Quantity (Q) on horizontal axis.
• Plot several (P, Q) points from schedules and draw smooth lines through them.
• Mark equilibrium point (P*, Q*). When illustrating shifts, draw the original curves faintly and the new curve with an arrow showing direction of shift; mark the new equilibrium.

Why this matters

Schedules and curves are the basic tools to analyze how markets respond to price changes and policy interventions (taxes, subsidies, price controls), and to predict effects on quantity exchanged and welfare measures (consumer/producer surplus).

Fig 3 — Educational Diagram: Excess Demand (Shortage) and Excess Supply (Surplus)

Definitions: Excess demand (shortage) occurs when, at a given price, quantity demanded (Qd) exceeds quantity supplied (Qs). Excess supply (surplus) occurs when Qs exceeds Qd at a given price.

Why they arise: They arise when price is away from the market-clearing (equilibrium) price. If price is set below equilibrium, demand rises and supply falls — creating a shortage. If price is set above equilibrium, supply rises and demand falls — creating a surplus. Other causes include sudden shifts in demand or supply (e.g., tastes, income, input costs), price controls (ceilings/floors), and time lags in adjustment.

Adjustment mechanism (price mechanism): Market forces push price toward equilibrium.

• Shortage (Qd > Qs): Buyers compete; sellers raise price. As price rises, Qd falls and Qs rises until Qd = Qs.
• Surplus (Qs > Qd): Sellers compete; they lower price. As price falls, Qd rises and Qs falls until Qd = Qs.

When shortages/surpluses persist: If prices are rigid (due to government price controls, long-term contracts, or information problems), the adjustment cannot occur and shortages/surpluses persist. Shortages can lead to rationing, queues, black markets; surpluses can lead to unsold inventories, waste, or government purchases.

Welfare effects: Persistent shortages and surpluses reduce allocative efficiency. Shortages can create deadweight loss via unmet demand and illegal market activity; surpluses create wasteful production and storage costs.

Illustrative numeric intuition: For any price P, excess demand = Qd(P) - Qs(P). If positive, there is a shortage; if negative, there is a surplus. The equilibrium price P* is where Qd(P*) = Qs(P*).

Fig 4 — Educational Diagram: Price Adjustment Mechanism and Stability of Equilibrium

What is the price adjustment mechanism?
The price adjustment mechanism is the process by which market price changes in response to excess demand or excess supply, pushing the market toward (or away from) the equilibrium where quantity demanded equals quantity supplied.

Basic logic
If at a given price P there is excess demand (Qd > Qs), the price tends to rise. If there is excess supply (Qs > Qd), the price tends to fall. The speed and pattern of these adjustments determine whether the market price converges to the equilibrium price (stable), oscillates around it, or diverges away (unstable).

Linear demand and supply (for exposition)
Let demand and supply be linear:

• Qd = a − bP, with b > 0
• Qs = c + dP, with d > 0

The static equilibrium (market-clearing) price and quantity are:

• P* = (a − c) / (b + d)
• Q* = a − bP* = c + dP*

Continuous-time price adjustment
A common specification is that the instantaneous rate of change of price is proportional to excess demand:

dP/dt = λ (Qd − Qs) = λ[(a − c) − (b + d)P], where λ > 0 is an adjustment speed parameter.

This is a first-order linear ODE. Its solution can be written as:

P(t) = P* + (P(0) − P*) exp[−λ(b + d) t]

Since λ(b + d) > 0, the exponential term decays → 0 as t → ∞. Thus the continuous adjustment model is stable: price converges monotonically and exponentially to P*.

Discrete-time price adjustment
If price is updated in discrete steps (periods), a simple rule is:

P_{t+1} = P_t + λ(Qd_t − Qs_t) = (1 − λ(b + d)) P_t + λ(a − c).

Stability of the fixed point P* requires the absolute value of the autoregressive coefficient to be less than 1:

|1 − λ(b + d)| < 1 ↔ 0 < λ(b + d) < 2.

If λ(b + d) is small (gentle adjustment), price converges to P*. If λ(b + d) = 2, the system oscillates with constant amplitude. If λ(b + d) > 2, the system oscillates with growing amplitude and diverges (unstable).

Cobweb model (expectations + production lag)
In many real markets (agriculture) supply decisions are based on the previous period's price (because of production lag). Suppose producers set Qs_t = c + d P_{t−1} and demand is Qd_t = a − b P_t. Market clearing in period t gives:

P_t = (a − c)/b − (d/b) P_{t−1}.

This is an AR(1) process. Stability criterion: |d/b| < 1.

• If |d/b| < 1 → convergent oscillations toward equilibrium (prices and quantities spiral in).
• If |d/b| = 1 → persistent oscillation (no damping).
• If |d/b| > 1 → divergent oscillations (spiral out), generating large price/quantity swings.

Economic intuition for stability conditions
- In the discrete adjustment model, if prices are changed too aggressively (λ large) relative to how responsive supply and demand are (b + d), overshooting creates oscillations and possibly divergence.
- In the cobweb model, if supply is very responsive to expected price relative to demand responsiveness (d large relative to b), the system tends to overshoot and oscillate away.

Role of rigidities and expectations
Real markets may have price/wage rigidities (sticky prices), gradual adjustment, inventory behavior, or adaptive/ rational expectations. These modify dynamics: sticky prices can slow or prevent convergence; adaptive expectations may produce cobweb-like cycles; forward-looking rational expectations can stabilize (or destabilize) depending on information and contracts.

Summary
Price adjustment mechanisms describe how prices respond to disequilibrium. Continuous adjustment with proportional response is typically stable. Discrete updating can be stable, oscillatory, or unstable depending on adjustment speed and slopes of supply and demand. The cobweb model shows how production lags and expectations can produce converging, persistent, or diverging cycles.

Fig 5 — Educational Diagram: Shifts in Demand: Effect on Equilibrium

What is a shift in demand? A shift in the demand curve means that at every price the quantity demanded changes because of changes in non-price determinants (income, tastes, prices of related goods, expectations, number of buyers, etc.). A rightward shift means demand increases; a leftward shift means demand decreases. This is different from a movement along the demand curve, which is caused only by a change in the price of the good.

Effect on market equilibrium (basic case — supply unchanged)

• Start from an initial equilibrium where demand D and supply S meet at point E (with price P* and quantity Q*).
• If demand increases (D shifts right to D'), the new intersection with the same supply curve S is at E'. The new equilibrium has a higher price (P' > P*) and a higher quantity (Q' > Q*).
• If demand decreases (D shifts left to D''), the new equilibrium price and equilibrium quantity both fall (P'' < P*, Q'' < Q*).

Intuition: More willingness to buy at each price (increase in demand) creates excess demand at the original price. Buyers bid the price up, suppliers respond by supplying more, and a new higher price and larger quantity clear the market. The opposite happens when demand falls.

Special cases (supply shapes matter):

• If supply is perfectly inelastic (vertical supply — fixed quantity), a shift in demand changes only price: quantity stays the same, price rises (for an increase in demand) or falls (for a decrease).
• If supply is perfectly elastic (horizontal supply — price fixed by market), a shift in demand changes only quantity: price remains unchanged, quantity increases (for rightward shift) or decreases (for leftward shift).
• If supply is upward sloping (normal case), both price and quantity move in the same direction as the demand shift.

Comparative-statics with linear curves (useful for calculations): Let demand be P = a - bQ and supply be P = c + dQ, where a,c,b,d > 0. Equilibrium satisfies a - bQ = c + dQ.

Solve: Q* = (a - c) / (b + d), and P* = (ad + bc) / (b + d).

If demand increases by raising 'a' to 'a + Δa' (a rightward shift), the new equilibrium changes by:

dQ*/da = 1/(b + d) > 0 (so Q rises); dP*/da = d/(b + d) > 0 (so P rises).

Practical implications: The size of the change in equilibrium price and quantity depends on the slopes (elasticities) of demand and supply. If supply is very inelastic, a demand increase mainly raises price. If supply is highly elastic, a demand increase mainly raises quantity.

Fig 6 — Educational Diagram: Shifts in Supply: Effect on Equilibrium

What is a shift in supply? A shift in the supply curve means that, at every price, the quantity supplied changes. A rightward shift (outward) means suppliers are willing to supply more at every price; a leftward shift (inward) means they supply less at every price. Shifts are caused by non-price factors: input costs, technology, taxes/subsidies, number of sellers, expectations, natural events, etc.

Effect on market equilibrium (intuitive)

• If supply increases (shift right) while demand is unchanged: equilibrium price falls and equilibrium quantity rises. Consumers buy more at a lower price (movement along the demand curve).
• If supply decreases (shift left) while demand is unchanged: equilibrium price rises and equilibrium quantity falls.
• Important distinction: a change in supply is a shift of the supply curve; a change in price (holding the curve fixed) causes movement along the demand curve.

Algebraic (linear) illustration

Let demand: Qd = m - nP (m, n > 0) and supply: Qs = c + dP (d > 0). Equilibrium requires Qd = Qs, so

P* = (m - c) / (n + d)

and

Q* = (md + cn) / (n + d)

If supply shifts out by an amount Δc (so new supply is Qs' = c + Δc + dP), the new equilibrium price and quantity are

P' = (m - (c + Δc)) / (n + d) = P* - Δc / (n + d)

Q' = Q* + n·Δc / (n + d)

Thus an outward shift (Δc > 0) lowers price by Δc/(n+d) and raises quantity by n·Δc/(n+d). A leftward shift (Δc < 0) has the opposite effects.

Special cases

• If supply is perfectly elastic (horizontal), a shift changes equilibrium price directly (new horizontal level) and quantity adjusts infinitely at that price in the simple model; in practice, a horizontal supply means price is fixed by suppliers, so any increase in supply lowers price to the new horizontal level.
• If supply is perfectly inelastic (vertical), quantity supplied is fixed; a supply reduction (vertical shift left) reduces equilibrium quantity and raises price sharply.

Key takeaway: With demand held constant, a rightward shift in supply reduces equilibrium price and increases equilibrium quantity; a leftward shift raises price and reduces quantity. The magnitude depends on the slopes (responsiveness) of supply and demand.

Fig 7 — Educational Diagram: Simultaneous Shifts in Demand and Supply

What it means
Simultaneous shifts occur when both the demand curve and the supply curve move at the same time because of different economic events. The new market equilibrium depends on the direction and magnitude of each shift.

Why it matters
When both curves shift, one variable (price or quantity) may change in a predictable direction while the other can be ambiguous — its direction depends on which shift is stronger.

Intuitive rules for the four basic combinations

• Demand increases, Supply increases: Equilibrium quantity (Q*) definitely rises. Equilibrium price (P*) is ambiguous — it rises if demand shifts more than supply, falls if supply shifts more, and remains unchanged if shifts are equal in effect.
• Demand decreases, Supply decreases: Equilibrium quantity definitely falls. Price is ambiguous (rises if supply falls more than demand, falls if demand falls more than supply).
• Demand increases, Supply decreases: Equilibrium price definitely rises. Quantity is ambiguous (depends on relative magnitudes).
• Demand decreases, Supply increases: Equilibrium price definitely falls. Quantity is ambiguous.

Algebraic (linear) illustration
Assume linear demand and supply:
Demand: Qd = a - bP (a,b > 0).
Supply: Qs = c + dP (c may be positive/negative; d > 0).
At equilibrium Qd = Qs:

P* = (a - c) / (b + d)

Q* = (cb + da) / (b + d)

Comparative statics (how equilibrium responds to shifts)
If demand shifts by changing parameter a (Δa > 0 means demand increases) and supply shifts by changing c (Δc > 0 means supply increases), the partial derivatives show directional effects:

• ∂P*/∂a = 1/(b + d) > 0 (an increase in demand raises price)
• ∂P*/∂c = -1/(b + d) < 0 (an increase in supply lowers price)
• ∂Q*/∂a = d/(b + d) > 0 (an increase in demand raises quantity)
• ∂Q*/∂c = b/(b + d) > 0 (an increase in supply raises quantity)

From these expressions you can see why quantity moves unambiguously when both curves shift in the same direction (both ∂Q*/∂a and ∂Q*/∂c are positive), while price can be ambiguous because ∂P*/∂a and ∂P*/∂c have opposite signs.

How to analyze a specific real situation

1. Identify which factors shift demand and which shift supply and in which direction.
2. Decide the likely magnitudes qualitatively (which effect is stronger?) or plug in numbers into a linear model if available.
3. Use the four-case logic above or the algebraic formulas to determine unambiguous vs ambiguous outcomes for price and quantity.

Key takeaway
Simultaneous shifts are resolved by combining the direction of each shift and, when necessary, comparing their magnitudes. Quantity often has an unambiguous change when both curves move the same way; price is often ambiguous except when shifts move price in the same direction (e.g., demand up & supply down → price up).

Fig 8 — Educational Diagram: Algebraic/Mathematical Determination of Equilibrium

Definition
Algebraic determination of equilibrium means finding the market equilibrium price (P*) and quantity (Q*) by equating the demand function and the supply function and solving algebraically.

Standard linear form
For linear demand and supply curves we usually write:

Demand: Qd = a - bP

Supply: Qs = c + dP

where a, b, c, d are positive constants, Q is quantity and P is price. b (>0) is the slope parameter of demand (how quantity demanded responds to price) and d (>0) is the slope parameter of supply.

Algebraic procedure

• Set quantity demanded equal to quantity supplied: Qd = Qs.
• Substitute the functional forms: a - bP = c + dP.
• Solve for the equilibrium price P*:

a - bP = c + dP   ⇒   a - c = (b + d)P   ⇒   P* = (a - c)/(b + d).

Once P* is found, substitute back to get equilibrium quantity Q*:

Q* = a - bP* = c + dP*.

Interpretation and conditions
If a > c then P* > 0. The solution is unique for linear, monotonic curves (b, d > 0). For non-linear functions, set Qd(P) = Qs(P) and solve the resulting equation (may yield multiple roots; choose economically meaningful positive P and Q).

Comparative statics (how equilibrium moves)
If demand shifts (a → a'), new P* = (a' - c)/(b + d). The change in equilibrium price from a change Δa is ΔP = Δa/(b + d). Similarly, a supply intercept change (c → c') changes P* by ΔP = -Δc/(b + d). This shows how sensitivity of P* to shifts depends on the sum of slopes (b + d).

Extensions
For non-linear curves (e.g., Qd = A - B P^2, Qs = C + D P), set A - B P^2 = C + D P and solve the polynomial for P. Select the economically relevant root(s).

Assumptions
Perfect competition (price-takers), continuous and downward-sloping demand and upward-sloping supply, no externalities, and market clears at intersection.

Fig 9 — Educational Diagram: Taxes, Subsidies and Their Effects on Equilibrium

Overview
Taxes and subsidies are government interventions that change prices received by sellers and/or paid by buyers and therefore change market equilibrium (price and quantity). Taxes raise the buyer price or reduce the seller price (or both), reducing quantity; subsidies lower buyer price or raise seller price (or both), increasing quantity.

Types of taxes
Specific (per‑unit) tax: a fixed amount t added per unit sold. Ad valorem (percentage) tax: a percentage τ of the transaction price.

How a per‑unit tax affects equilibrium
- Graphically: supply curve shifts vertically upward by the tax amount t (if tax legally on sellers) or the demand curve shifts downward by t (if taxed on buyers). Economically the result is the same: a "wedge" t between price paid by buyers (Pb) and price received by sellers (Ps), where Pb − Ps = t.
- New equilibrium has lower quantity Q' and different buyer and seller prices: Pb > P* > Ps (P* = initial equilibrium price without tax).
- Tax revenue = t × Q'.
- Deadweight loss (DWL): reduction in total surplus equals the triangular area representing mutually beneficial trades that no longer occur; DWL > 0 whenever Q' < Q*.

How a subsidy affects equilibrium
- Graphically: supply curve shifts vertically downward by subsidy s (if subsidy to producers) or demand shifts upward by s (if to consumers). A subsidy creates a wedge where sellers receive Ps and buyers pay Pb and Ps − Pb = s.
- New equilibrium quantity Q' > Q*; subsidy increases consumer and producer surplus but costs the government.
- Government expenditure = s × Q'.
- There is also a DWL because the marginal cost of some additional units exceeds their marginal benefit.

Incidence (who bears the burden?)
- Legal incidence (who sends money to government) is not the same as economic incidence (who actually bears the burden). The division depends on price elasticities of demand (Ed, absolute value) and supply (Es): the relatively more inelastic side bears a larger share of the tax burden.

Elasticity rule for per‑unit tax
- Consumer share of tax ≈ Es / (Es + |Ed|) × t
- Producer share of tax ≈ |Ed| / (Es + |Ed|) × t

Summary of effects
- Tax: quantity falls, buyer price rises, seller price falls, government revenue collected, total surplus falls by tax revenue + DWL.
- Subsidy: quantity rises, buyer price falls, seller price rises, government pays subsidy, total surplus net of government cost falls by DWL (unless external benefits justify it).

Fig 10 — Educational Diagram: Welfare Effects: Consumer and Producer Surplus (Related Concepts)

Overview

Welfare analysis in a competitive market measures gains to buyers and sellers from trade. Two central concepts are consumer surplus (CS) and producer surplus (PS). Together they form total surplus, a summary measure of market welfare under standard assumptions (perfect competition, no externalities, well-defined property rights).

Consumer surplus (intuitive)

Consumer surplus is the difference between what buyers are willing to pay for a good (their marginal benefit) and what they actually pay (market price). Graphically it is the area under the demand curve and above the price, up to the traded quantity.

Producer surplus (intuitive)

Producer surplus is the difference between the market price received and the minimum price at which sellers are willing to supply (their marginal cost). Graphically it is the area above the supply curve and below the price, up to the traded quantity.

Total surplus and efficiency

Total surplus = CS + PS. In a perfectly competitive market at equilibrium price and quantity, total surplus is maximized — meaning resources are allocated efficiently (no mutually beneficial trades are left undone). Any policy or distortion that reduces total surplus creates a deadweight loss (DWL), the net loss of welfare compared to the free-market equilibrium.

How to compute (area interpretation)

If the demand curve gives the maximum willingness to pay for each unit and the supply curve gives the minimum acceptable price (marginal cost), CS is the area between demand curve and price line, PS is the area between price line and supply curve. For a single unit or discrete units this is the difference of willingness-to-pay and price (or price and cost).

Effects of policy and shocks

• Price ceiling (e.g., rent control): Price set below equilibrium increases consumer surplus for those who can buy at the low price but reduces producer surplus and creates a shortage and DWL (lost trades). Overall total surplus typically falls.
• Price floor (e.g., minimum wage or MSP above equilibrium): Price set above equilibrium raises producer surplus for those who sell at the higher price but reduces consumer surplus and causes excess supply (surplus) and DWL.
• Per-unit tax: Tax creates a wedge between price buyers pay and price sellers receive, reduces traded quantity, shrinks CS and PS, raises government revenue (rectangle area) but creates DWL (triangle area) because fewer mutually beneficial trades occur.
• Subsidy: Lowers price to buyers and raises price received by sellers (if subsidy paid per unit). It increases traded quantity, increases CS and PS but requires government spending; it also creates DWL because subsidy encourages some trades where cost exceeds benefit.
• Shifts in demand or supply: A rightward shift in demand increases equilibrium price and quantity, typically increasing PS and changing CS depending on slope — total surplus may increase if more mutually beneficial trades occur.

Limitations and assumptions

• CS and PS rely on underlying demand and supply representing marginal benefits and marginal costs.
• They ignore distributional concerns—total surplus could increase while one side is made much worse off.
• Externalities, public goods, information problems and market power break the efficiency result.

Summary

Consumer and producer surplus provide simple, graphical and quantitative measures of welfare changes from market outcomes, policies and shocks. Comparing CS+PS across scenarios tells us whether a change raises or lowers total welfare and where losses occur (buyers, sellers), while DWL quantifies efficiency losses from distortions.

Fig 11 — Educational Diagram: Dynamic Adjustments and Time Dimensions

What the topic covers
Dynamic adjustments describe how prices and quantities move over time toward (or away from) market equilibrium after a shock. Time dimensions explain that the speed and form of adjustment depend on the length of the decision horizon: market period (very short run), short run and long run. Supply responsiveness (elasticity) typically increases as we move from market period → short run → long run, so adjustment outcomes differ across these periods.

Mechanics of adjustment

• Excess demand (shortage): Qd > Qs → upward pressure on price. Higher price reduces quantity demanded and encourages more supply (or entry over time) until equilibrium is restored.
• Excess supply (surplus): Qs > Qd → downward pressure on price. Lower price increases demand and reduces supply (or forces exit) until equilibrium is restored.
• Adjustment channels: price changes, quantity changes (inventory drawdown/build-up), entry/exit of firms, adjustment of capital/labor

Time dimensions and their features

• Market period (very short run): Some supplies are fixed (vertical supply curve). Prices absorb the shock; quantities cannot adjust. Example: fish just landed — quantity fixed today.
• Short run: Some inputs/capacity fixed, other inputs variable. Supply is upward sloping but inelastic relative to long run. Firms adjust output by using existing capacity more intensively or changing labor.
• Long run: All inputs are variable, firms can enter or exit the industry, capacity can be adjusted. Supply is more elastic; prices return closer to competitive long-run equilibrium (normal profit level for firms).

Dynamic models (intuition and simple formulations)

• Basic equilibrium condition: Qd(P*) = Qs(P*). Deviation is excess demand: ED(P) = Qd(P) − Qs(P).
• Tâtonnement / discrete price adjustment: P_{t+1} = P_t + α[Qd(P_t) − Qs(P_t)], where α > 0 is an adjustment speed parameter. If ED > 0 price rises next period; if ED < 0 price falls.
• Continuous-time version: dP/dt = k · [Qd(P) − Qs(P)], k > 0. Price changes at a rate proportional to excess demand.
• Cobweb (production lag) model: when supply in period t is based on expected/observed price in t−1, oscillations may occur. With linear forms Qs_t = c + s·P_{t−1} and demand P_t = a − d·Q_t, price evolves as P_t = (a − d·c) − (d·s)·P_{t−1}. Stability depends on |d·s| < 1 (convergent), =1 (neutral), >1 (divergent).

Stability condition (linear example)
If Qd = A − B·P and Qs = C + D·P, discrete adjustment ΔP = α[(A − B·P_t) − (C + D·P_t)] = α[(A−C) − (B+D)P_t]. The steady price P* = (A−C)/(B+D). For the discrete scheme to converge monotonically to P*, a standard condition is 0 < α(B+D) < 2 (equivalently |1 − α(B+D)| < 1).

Key implications for policy/markets

• Short-run shocks often show large price volatility where supply is inelastic (e.g., perishable goods, seats on a flight).
• Long-run adjustment (entry/exit, capacity changes) reduces volatility but takes time; policy meant to stabilize markets must consider the relevant time horizon.
• Production lags can cause oscillations (cobweb); forecasting and contracts can reduce instability.

Fig 12 — Educational Diagram: Graphical Methods and Diagrammatic Analysis

What it is: Graphical methods and diagrammatic analysis is the use of supply and demand diagrams to find and explain market equilibrium (the price and quantity where demand equals supply) and to analyse effects of shocks (shifts), policy instruments (taxes, subsidies, price controls) and changes in elasticities. Diagrams make abstract algebraic results intuitive and show welfare effects (consumer surplus, producer surplus, deadweight loss).

How to draw and read the basic diagram:

• Axes: vertical axis = Price (P), horizontal axis = Quantity (Q).
• Draw the demand curve (D) sloping downwards (higher P → lower Q demanded) and the supply curve (S) sloping upwards (higher P → higher Q supplied).
• Equilibrium point E is where D and S intersect. The coordinates (P*, Q*) are the equilibrium price and quantity.
• Movement along a curve = change in quantity supplied/demanded due to a change in price. Shift of a curve = change in supply/demand at every price (caused by non‑price factors: income, technology, input costs, taxes, preferences).

Diagrammatic analysis steps:

1. Identify whether the shock/policy changes demand or supply (or both).
2. Shift the appropriate curve(s) right (increase) or left (decrease).
3. Find the new intersection; label new equilibrium (P1, Q1) and compare to original (P0, Q0).
4. Show and compute surplus/welfare changes: consumer surplus (CS), producer surplus (PS), government revenue, and deadweight loss (DWL) where relevant.

Key comparative statics explained diagrammatically:

• Demand shift right → higher P and higher Q (usually). Demand shift left → lower P and lower Q.
• Supply shift right → lower P and higher Q. Supply shift left → higher P and lower Q.
• Price ceiling (binding) below P* → shortage (Qd > Qs), black markets, loss of welfare; price floor above P* → surplus (Qs > Qd), possible government purchase.
• Tax: supply shifts up by the tax amount (or a parallel wedge between buyer and seller prices). Quantity falls; consumers pay higher price than producers receive. Deadweight loss equals the triangle of lost mutually beneficial trades.
• Subsidy: supply shifts down (or buyer price lower than seller price); quantity rises; government pays subsidy per unit; possible DWL if market distortion.
• Elasticities matter: incidence of tax/subsidy depends on relative price elasticities of demand and supply — the less elastic side bears more of the tax burden.

Simple numeric example (linear curves):

Let Qd = 100 − 2P and Qs = 20 + 3P. Equilibrium: set Qd = Qs → 100 − 2P = 20 + 3P → 80 = 5P → P* = 16. Then Q* = 100 − 2(16) = 68.

Using the same diagram you can show a rightward demand shift (e.g., to Qd' = 120 − 2P): intersection moves to a higher P and higher Q. Or impose a specific tax t on sellers: new supply Qs_t = 20 + 3(P − t) so the supply curve shifts up by t, reducing equilibrium Q and creating a price wedge.

Welfare areas on the diagram: mark consumer surplus as the area under the demand curve and above the market price up to Q* (a triangle for linear demand). Producer surplus is the area above the supply curve and below the market price up to Q*. Government revenue equals tax × quantity after tax (rectangle). Deadweight loss is the small triangle of lost trades between the pre‑tax and post‑tax quantities.

Fig 13 — Educational Diagram: Applications and Examples

Overview: Market equilibrium is the price and quantity where quantity demanded equals quantity supplied (Qd = Qs). The concept is useful for analysing how taxes, subsidies, price controls, import restrictions and other policies change prices, quantities and welfare (consumer surplus, producer surplus and deadweight loss).

How to find equilibrium (linear form): If demand and supply are given as price functions, for example
Demand: P = a - bQ
Supply: P = c + dQ

Set demand equal to supply to solve for equilibrium quantity and price:

• Q* = (a - c) / (b + d)
• P* = a - bQ* (or P* = c + dQ*)

Comparative statics: When an exogenous change occurs (shift in demand or supply), recompute equilibrium by substituting the shifted function. Typical applications:

• Tax on sellers (specific per unit tax t): supply shifts up by t. New supply: P = c + dQ + t. New Q = (a - c - t) / (b + d). Buyers pay a higher price; sellers receive price = Pbuyer - t. The difference between buyer price and seller price is the tax wedge.
• Subsidy s per unit: supply shifts down by s (or demand shifts up if subsidy to buyers). New supply: P = c + dQ - s; equilibrium quantity increases.
• Price ceiling (Pc): if Pc < P*, binding ceiling creates shortage = Qd(Pc) - Qs(Pc) and may cause rationing, queues or black markets.
• Price floor (Pf): if Pf > P*, binding floor creates surplus = Qs(Pf) - Qd(Pf) and may require public purchase (e.g., minimum support price).

Welfare effects: consumer surplus (CS) and producer surplus (PS) change with policies. Tax and price controls typically create deadweight loss (DWL) equal to the value of mutually beneficial trades that no longer occur.

Incidence (who bears the burden?): Tax burden is shared between consumers and producers. The relative burden depends on price elasticities of demand and supply (more inelastic side bears larger share).

Fig 14 — Educational Diagram: Comparative Statics and Policy Implications

What is comparative statics? Comparative statics is the method of comparing two market equilibria — one before and one after a change in an exogenous variable (tax, subsidy, technology, tastes, input price, etc.). It shows how equilibrium price and quantity change when supply or demand shifts.

Steps in comparative-static analysis

• Identify the exogenous change (what causes supply or demand to shift).
• Determine direction of shift (right = increase, left = decrease).
• Find the new intersection of demand and supply to get the new equilibrium price and quantity.
• Interpret economic effects: price paid by buyers, price received by sellers, quantity traded, government revenue, and welfare effects (consumer surplus, producer surplus, deadweight loss).

Algebraic (linear) example — before and after a per-unit tax:

Suppose demand: Qd = a - bP_b and supply (from sellers) without tax: Qs = c + dP_s. With a per-unit tax t on sellers, the price sellers receive P_s = P_b - t. Equilibrium after tax satisfies:

a - bP_b = c + d(P_b - t).

Solving gives buyer price after tax: P_b = (a - c + d t)/(b + d). Original price (t = 0) was P_b0 = (a - c)/(b + d). So the increase in buyer price is ΔP_b = d t/(b + d).

Change in seller price received: ΔP_s = ΔP_b - t = - b t/(b + d). Thus buyers bear d/(b+d) of tax and sellers bear b/(b+d).

Interpretation in elasticity terms

Tax incidence depends on elasticities of demand (Ed) and supply (Es). The fraction of tax borne by buyers ≈ Es/(Es + |Ed|) and the fraction borne by sellers ≈ |Ed|/(Es + |Ed|). The less elastic side bears more of the tax burden.

Welfare effects

• Government revenue (per unit tax) = t × Q_after.
• Deadweight Loss (DWL) from a per-unit tax ≈ 1/2 × t × (Q_before − Q_after). This triangle measures lost trades that would have been mutually beneficial.
• Subsidies increase quantity but create DWL paid by taxpayers; price controls (ceilings/floors) create shortages or surpluses and reduce welfare.

Policy implications

• Taxes: Raise revenue but distort market outcomes. Choose tax design knowing incidence — taxing inelastic goods raises revenue with smaller quantity loss (but may be regressive).
• Subsidies: Encourage consumption/production (e.g., fertilizers) but cost taxpayers and can create inefficiency and overuse.
• Price ceilings (rent control): Benefit some consumers via a lower price but cause shortages, black markets, lower quality and reduced investment in supply.
• Price floors (minimum support prices): Protect producers' incomes but can create surpluses that governments must buy or waste (storage costs, distortions).
• Trade policy (tariffs/quotas): Protect domestic producers but raise domestic prices and reduce consumer surplus; create deadweight loss and retaliation risks.
• Policy design should weigh equity vs efficiency: targeted transfers often better than broad subsidies or price controls.

How to present this in class

• Use a simple linear demand-supply algebraic example to compute exact price/quantity changes under a tax or subsidy.
• Draw diagrams to show shifts, the tax wedge (vertical distance = t), areas of consumer/producer surplus, government revenue rectangle and DWL triangle.
• Discuss real-life examples to connect theory to policy trade-offs.