Micro math practice

Every skill in this set

Price elasticity of demandSupply & Demand

PED = %ΔQd / %ΔP

Report the absolute value and compare it with 1. Above 1 is elastic, so a price rise cuts total revenue; below 1 is inelastic, so a price rise raises it.

Marginal and average cost from a tableProduction, Cost & Perfect Competition

MC = ΔTC / ΔQ · ATC = TC / Q

Marginal is a difference between rows; average is a division within a row. Differencing an average or dividing a change is the standard error, and both produce believable numbers.

Marginal revenue productFactor Markets

MRP = MP × P (competitive product market)

Hire while MRP exceeds the wage, and stop where they are equal. That is the factor-market version of MR = MC and it decides every labor-demand question.

Price elasticity by the midpoint methodSupply & Demand

E = [ΔQ ÷ avg Q] / [ΔP ÷ avg P]

Dividing by the averages makes the answer identical whichever direction you compute it. Using the starting values gives two different numbers for the same pair of points, which is why the midpoint method is the one the exam expects.

Income and cross-price elasticitySupply & Demand

E_i = %ΔQ / %Δincome · E_xy = %ΔQ_x / %ΔP_y

For these two the SIGN is the answer, not the magnitude. Positive income elasticity means normal, negative means inferior. Positive cross-price means substitutes, negative means complements. Taking absolute values throws the finding away.

Total revenue and the elasticity testSupply & Demand

TR = P × Q

Revenue is the practical payoff of elasticity. A price change moves P and Q in opposite directions, and which one wins is exactly what elastic and inelastic mean.

Average and marginal cost from totalsProduction, Cost & Perfect Competition

ATC = TC/Q · AVC = TVC/Q · AFC = TFC/Q · MC = ΔTC/ΔQ

Marginal cost is the difference between consecutive totals, not a total divided by a quantity. Computing MC as TC/Q gives average total cost and answers a different question.

Accounting versus economic profitProduction, Cost & Perfect Competition

accounting = revenue − explicit · economic = revenue − explicit − implicit

Implicit costs are real even though no payment is made for them. Omitting the owner’s forgone salary is the most common error in this topic and it always overstates how well the business is doing.

Monopoly quantity and price from linear demandImperfect Competition

P = a − bQ → MR = a − 2bQ · set MR = MC for Q, then read P off DEMAND

Marginal revenue has the same intercept and twice the slope. And the price comes from the demand curve at the chosen quantity — reading it off MR is the classic monopoly error.

Deadweight loss triangleImperfect Competition

DWL = ½ × (P − MC) × (Q_efficient − Q_actual)

The triangle is bounded by demand above and marginal cost below, between the actual and efficient quantities. Drawing it against ATC instead of MC gives the wrong area.

Marginal factor cost under monopsonyFactor Markets

MFC = Δ(wage × workers) / Δworkers

A monopsonist must pay the new higher wage to everyone already employed, so MFC is the new wage PLUS all the raises. It exceeds the wage substantially, not marginally.

Corrective tax and externality deadweight lossMarket Failure & Government

corrective tax = marginal external cost · DWL = ½ × external cost × (Q_market − Q_optimal)

The tax equals the external cost per unit — not the total damage and not the resulting price change. And the socially optimal quantity is almost never zero.

Least-cost input combinationFactor Markets

MP_L / P_L = MP_K / P_K

Equalize output per DOLLAR, not per unit. An input with a higher marginal product can still be the worse buy if it costs proportionally more.

Common questions