📐 Micro Formula Sheet

All key formulas for ECON1001 / ECOS2001 — print-friendly revision reference

Supply and Demand

Formula	Description
Q_D = a − bP	Demand function (linear)
Q_S = c + dP	Supply function (linear)
Equilibrium: Q_D = Q_S	Solve for P* and Q*
Excess demand = Q_D − Q_S (negative = surplus)	At a given price
Excess supply = Q_S − Q_D (positive = surplus)	At a given price

Formula	Description
PED = %ΔQ_D / %ΔP	Price elasticity of demand (negative)
PES = %ΔQ_S / %ΔP	Price elasticity of supply (positive)
YED = %ΔQ_D / %ΔIncome	Income elasticity (+ve = normal, −ve = inferior)
XED = %ΔQ_Dx / %ΔP_y	Cross-price elasticity (+ve = substitutes, −ve = complements)
Point elasticity: PED = (dQ/dP) × (P/Q)	For demand function Q = f(P)
Midpoint method: PED = [(Q₂−Q₁)/avg Q] / [(P₂−P₁)/avg P]	Avoids direction bias

Formula	Description
CS = ½ × base × height (triangle)	Area under demand, above price
CS = WTP − Price (per unit)	Marginal benefit minus price paid
MB for unit n: substitute q = n into MB equation	e.g. MB = 150 − 2q → at q=10: MB = $130
PS = ½ × base × height (triangle)	Area above supply, below price
Total surplus = CS + PS	Social gains from trade
DWL = ½ × (P_distortion − MC) × ΔQ	Deadweight loss triangle
Rule of Half: ΔCS = ΔCost × Q₀ + ½ × ΔCost × ΔQ	Infrastructure CBA

Step	Description
1. Rewrite each demand as Q = f(P)	Invert the inverse demand
2. Add: Q_market = Q_A + Q_B	Sum at each price
3. Invert back to P = f(Q)	Get market inverse demand
Note: kink at price where one consumer drops out	Curve steepens above that price

Formula	Description
MPL = ΔTP / ΔL	Marginal product of labour
APL = TP / L	Average product of labour
MC = ΔTC / ΔQ = ΔVC / ΔQ	Marginal cost
ATC = TC / Q = AFC + AVC	Average total cost
AFC = TFC / Q	Always declining
AVC = TVC / Q	U-shaped
MC = P_L / MPL	Cost from labour productivity
Profit = TR − TC = (P − ATC) × Q
Profit max: MR = MC	Universal rule

Formula	Description
P = MR = AR	Price-taking firm
Short-run supply: MC above AVC	Shutdown if P < AVC
Long-run: P = min ATC, π = 0	Free entry eliminates profit
Productive efficiency: P = min ATC
Allocative efficiency: P = MC

Formula	Description
P = a − bQ → MR = a − 2bQ	MR has twice the slope
Profit max: MR = MC	Find Q, then P from demand
Lerner index: L = (P − MC)/P = 1/\|PED\|	Market power measure
DWL = ½ × (P_m − MC) × (Q_c − Q_m)	Efficiency loss
3rd degree PD: MR₁ = MR₂ = MC	Equate MR across markets
P(1 − 1/\|ε\|) = MC	Optimal price with elasticity

Formula	Description
Tax incidence: consumer share ≈ PES / (PES + \|PED\|)	Less elastic side bears more
Tax revenue = tax × Q_taxed
Subsidy: ΔCS + ΔPS = subsidy cost − DWL	Overproduction creates DWL

Concept	Description
Nash Equilibrium: no unilateral deviation is profitable	Check all best responses
Dominant strategy: best regardless of opponent's choice
Cournot: q = (a − c) / [b(n+1)] each firm*	n symmetric firms
Stackelberg leader: q₁ = (a−c) / 2b	Double the Cournot quantity
Bertrand: P = MC	Price competition with identical goods

Formula	Description
Budget constraint: P₁x₁ + P₂x₂ = m
Optimal: MRS = P₁/P₂	Tangency condition
MRS = −MU₁/MU₂ = −(∂U/∂x₁)/(∂U/∂x₂)
Cobb-Douglas U = x₁^a x₂^b: x₁ = am/(P₁(a+b))*	Marshallian demand
Slutsky: ∂x/∂P = substitution effect + income effect
CV = e(P⁰,u⁰) − e(P¹,u⁰)	Compensating variation