ECON 351 FORMULAS (Midterm 2)

Tax wedge

Pd = Ps + tax

Tax revenue

Tax revenue = tax per unit × Q′

Subsidy wedge

Pd = Ps − subsidy; equivalently, Ps = Pd + subsidy

Government cost of a subsidy

Subsidy cost = subsidy per unit × Q′

Marginal social cost

MSC = MC + MEC

Marginal social benefit

MSB = MB + MEB

Socially optimal condition with a negative externality

MSC = MB

Socially optimal condition with a positive externality

MSB = MC

Corrective tax for a negative externality

Tax = MEC at Qsocially optimal

Corrective subsidy for a positive externality

Subsidy = MEB at Qsocially optimal

Negative-externality deadweight loss

DWL = ½ × MEC(Qmarket) × (Qmarket − Qsocially optimal)

Positive-externality deadweight loss

DWL = ½ × MEB(Qmarket) × (Qsocially optimal − Qmarket)

Total cost

C(Q) = FC + VC(Q)

Average cost

AC = C(Q) ÷ Q

Average variable cost

AVC = VC(Q) ÷ Q

Marginal cost

MC = dC(Q) ÷ dQ

Total revenue

R(Q) = P(Q) × Q

Marginal revenue

MR = dR(Q) ÷ dQ

Marginal revenue with linear demand

If P = a − bQ, then MR = a − 2bQ

Profit

Profit = total revenue − total cost

Profit using average cost

Profit = (P − AC) × Q

Profit using producer surplus

Profit = producer surplus − fixed cost

Price elasticity of demand

E = (dQ ÷ dP) × (P ÷ Q)

Lerner Index

L = (P − MC) ÷ P = −1 ÷ E

Third-degree price discrimination

MR1 = MR2 = MC, and profit = R1(Q1) + R2(Q2) − C(Q1 + Q2)