AP Microeconomics — Cheatsheet
Formulas, exam-day tips, and key terms on one page.
Formulas & relationships
Utility-maximizing rule
MUx / Px = MUy / Py
A consumer maximizes utility when the marginal utility per dollar is equal for every good. If MUx/Px > MUy/Py, buy more of X (and less of Y) until they equalize.
Opportunity cost along a PPC
OC of gaining Good X = (units of Good Y given up) / (units of Good X gained)
Read the trade-off between two points directly off the axes. Constant along a straight-line PPC; increasing along a bowed-out PPC.
Opportunity cost from output data
OC of 1 unit of Good A = (output of Good B) / (output of Good A) → "Other over Own"
Lower opportunity cost = comparative advantage. With input (per-unit time) data instead, flip to "Own over Other."
Single-shift outcomes
Demand ↑ ⇒ P ↑, Q ↑ · Demand ↓ ⇒ P ↓, Q ↓ · Supply ↑ ⇒ P ↓, Q ↑ · Supply ↓ ⇒ P ↑, Q ↓
With one shift, both price and quantity are determined. With two shifts, one of the two becomes ambiguous.
Price elasticity of demand
Ed = (% change in quantity demanded) / (% change in price)
Elastic if |Ed| > 1, inelastic if |Ed| < 1, unit elastic if |Ed| = 1. Total-revenue test: cut price to raise revenue when elastic; raise price to raise revenue when inelastic.
Surplus and efficiency
Total surplus = Consumer surplus + Producer surplus (maximized at competitive equilibrium)
Any binding price control reduces the traded quantity below equilibrium, creating deadweight loss = the surplus on the forgone mutually beneficial trades.
Key cost relationships
TC = FC + VC · ATC = TC/Q = AFC + AVC · MC = ΔTC / ΔQ
Marginal cost pulls the averages: when MC is below ATC, ATC falls; when MC is above ATC, ATC rises; MC crosses ATC (and AVC) at their minimums.
Profit and the decision rules
Profit-max: MR = MC · Economic profit = (P − ATC) × Q · Shut down if P < AVC
Produce where MR = MC, then check profit against ATC and viability against AVC. Zero economic profit = normal profit (breaking even including opportunity cost).
The competitive firm’s conditions
Short run: P = MR = MC · Long-run equilibrium: P = MR = MC = minimum ATC (zero economic profit)
A price taker faces a horizontal demand curve, so MR = P. Free entry/exit competes economic profit away to zero in the long run.
Monopoly pricing
Profit-max: MR = MC, then set price from demand: P > MR = MC · Allocative efficiency would require P = MC
Because P > MC at the monopoly output, output is below the efficient level, creating deadweight loss. For linear demand, MR has the same intercept but twice the slope.
Long-run equilibrium features
MR = MC (profit-max) · Zero economic profit (P = ATC, tangency) · P > MC (inefficient) · excess capacity
Like monopoly: downward-sloping demand, MR < P, P > MC. Like perfect competition: easy entry drives long-run profit to zero. Unlike perfect competition: not at minimum ATC.
Reading the game
Dominant strategy: best choice no matter what the rival does · Nash equilibrium: no player gains by changing strategy alone
Analyze one firm at a time: fix the rival’s choice, pick this firm’s best response. Where both firms’ best responses coincide is the Nash equilibrium.
Factor hiring
MRP = MP × MR (= MP × P in a competitive product market) · Hire until MRP = MRC
MRP is the extra revenue from one more unit of the factor; MRC is its extra cost. In a competitive labor market MRC equals the market wage.
Competitive labor market equilibrium
Market: labor demand (ΣMRP) = labor supply → sets wage · Firm: hires where MRP = wage (MRC)
The market sets the wage; the wage-taking firm faces a horizontal labor-supply curve at that wage and hires until MRP falls to it.
Least-cost and profit-max input rules
Least-cost: MPL / PL = MPK / PK · Profit-max: MRPL / PL = MRPK / PK = 1
Equalizing marginal product per dollar minimizes cost for a given output; hiring each input until MRP = its price maximizes profit and satisfies the least-cost rule too.
Efficiency and externalities
Social optimum: MSB = MSC · Negative externality: MSC > MPC → overproduction · Positive externality: MSB > MPB → underproduction
A corrective tax equal to the external cost fixes overproduction; a subsidy equal to the external benefit fixes underproduction. Both push the market quantity to where MSB = MSC.
Classifying goods
Private: rival + excludable · Public: non-rival + non-excludable · Common resource: rival + non-excludable · Club: non-rival + excludable
Non-excludability drives the free-rider problem (public goods underprovided); rivalry plus non-excludability drives the tragedy of the commons (common resources overused).
Tax incidence and inequality measures
Burden falls more on the more inelastic side · Gini = 0 (perfect equality) → 1 (perfect inequality)
Tax revenue = per-unit tax × quantity traded after the tax. The Lorenz curve bowing farther from the 45° line means a higher Gini coefficient.
On the exam
- For utility-maximization problems, always convert to **marginal utility per dollar** (MU ÷ price) before comparing goods — never compare raw marginal utilities when prices differ. Buy from whichever good has the higher MU-per-dollar until they equalize and the budget is spent.
- Label PPC diagrams fully: both goods on the axes, and be explicit about whether a change is a **movement along** (reallocation) or a **shift/rotation** (capacity change). Biased technology rotates the curve along one axis — a favorite AP variation.
- On comparative-advantage free-response items, always (1) compute each party’s opportunity costs, (2) assign each good to the lower-cost producer, and (3) give a specific trade rate *between* the two costs. Showing the numbers, not just naming the winner, earns the points.
- For a **double shift**, one variable is always determinate and the other ambiguous. Identify the shared direction (both shifts pushing price *or* quantity the same way) — that variable is certain; the other depends on relative shift sizes.
- For cross-price and income elasticities, read the **sign** first: cross-price positive = substitutes, negative = complements; income positive = normal, negative = inferior. Magnitude tells you *how strong*, but the sign tells you *what kind*.
- On price-control graphs, show the **reduced quantity traded**, then mark the **deadweight-loss triangle** between the supply and demand curves at that quantity. Distinguish the **transfer** of surplus between groups from the **deadweight loss** that no one captures — the exam tests both.
- Remember the marginal-average rule: when **MC < ATC, ATC falls**; when **MC > ATC, ATC rises**; and **MC crosses ATC and AVC at their minimum points**. This lets you locate the minimum of the average curves directly on a graph.
- Run the two-step firm analysis: (1) find output where **MR = MC**, then (2) compare price to **ATC** for profit/loss and to **AVC** for the shutdown decision. Zero economic profit is *breaking even* (normal profit), not a loss — a distinction the exam tests directly.
- Draw the competitive firm with a **horizontal demand = MR = price** line and the U-shaped ATC/AVC/MC curves. In the long run, that price line is **tangent to minimum ATC**. Free-response prompts reward showing entry/exit driving profit to zero.
- Draw the monopoly graph with demand *above* MR, find output at MR = MC, then go **straight up to the demand curve** for price. Mark the deadweight-loss triangle between demand and MC from the monopoly quantity out to the efficient (P = MC) quantity.
- For monopolistic competition, draw it like a "shrunken monopoly": downward-sloping demand with MR below it, MR = MC for quantity, and in the long run the **demand curve tangent to ATC** (zero profit). Label the excess capacity gap between that output and minimum ATC.
- To solve a payoff matrix, analyze **one firm at a time**: hold the rival’s choice fixed and find that firm’s best response, then repeat. Where both best responses meet is the **Nash equilibrium**. Always identify dominant strategies before naming the equilibrium.
- The hiring rule **MRP = MRC** is the factor-market twin of the product-market rule MR = MC. In a competitive labor market, set **MRP = wage**. Always confirm whether the *product* market is competitive before using MRP = MP × P.
- Free-response items often pair a **market** labor diagram (setting the wage) with a **firm** diagram (MRP = wage). Show the wage determined in the market, then carry that horizontal wage line to the firm’s MRP curve to find how many workers it hires.
- For least-cost problems, compute **marginal product per dollar** (MP ÷ input price) for each input and shift toward the higher one until they equalize. Do not compare raw marginal products when input prices differ — always divide by price first.
- On externality graphs, draw both the private and social curves (MPC vs. MSC, or MPB vs. MSB), mark the market quantity and the optimal quantity where **MSB = MSC**, and shade the **deadweight-loss triangle** between them. State the corrective tax or subsidy as the **vertical distance** equal to the external cost or benefit.
- When a question describes a good, test it on **both** rivalry and excludability before classifying it. The **free-rider problem** stems from **non-excludability**; the **tragedy of the commons** stems from rivalry combined with non-excludability. Naming the right property earns the point.
- On tax graphs, show the tax as a **vertical wedge** between the price buyers pay and sellers receive, then identify each side’s share and the **deadweight-loss triangle**. For inequality, remember: Lorenz curve farther from the 45° line ⇒ **higher Gini ⇒ more inequality**.
How to get a 5
- Always label your axes! P and Q for product markets, Wage and Quantity of Labor for factor markets. Unlabeled axes result in zero points for the graph.
- Remember that 'Profit' implies Economic Profit (Accounting Profit minus Implicit/Opportunity Costs). Zero economic profit is a normal, sustainable outcome in the long run.
- For monopolies and monopolistically competitive firms, the MR curve is always below the Demand curve. To find price, find where MR=MC, then go UP to the Demand curve.
- Lump-sum taxes or subsidies affect fixed costs (ATC), changing profit but NOT changing the profit-maximizing quantity (MC is unaffected). Per-unit taxes/subsidies affect variable costs (MC and ATC), shifting output quantity.
Key terms
Law of Demand vs. Change in Demand — Law of Demand (Change in Quantity Demanded): Price changes, movement ALONG the curve. Change in Demand: Non-price determinant changes, SHIFT of the entire curve.
Price Elasticity of Demand (PED) — PED = %Δ Qd / %Δ P. If >1, elastic. If <1, inelastic. If =1, unit elastic.
Total Revenue Test — If Price and Total Revenue move in OPPOSITE directions, demand is elastic. If they move in the SAME direction, demand is inelastic.
Cross-Price Elasticity — Positive = Substitute goods (e.g., Coke & Pepsi). Negative = Complementary goods (e.g., hot dogs & buns).
Marginal Utility per Dollar — To maximize utility, a consumer should allocate spending so that: MUx / Px = MUy / Py.
Law of Diminishing Marginal Returns — As variable inputs (like labor) are added to fixed inputs (like capital), the marginal product of the variable input will eventually decline.
Profit-Maximizing Rule — A firm maximizes profit (or minimizes loss) by producing the quantity where Marginal Revenue = Marginal Cost (MR = MC).
Perfect Competition Characteristics — Many small firms, identical products, easy entry/exit, price takers (horizontal demand curve at the market price).
Shut-Down Rule — In the short run, a firm should shut down if Price falls below the minimum Average Variable Cost (P < AVC).
Monopoly Characteristics — Single seller, unique product, high barriers to entry, price maker (downward sloping demand, MR below demand).
Price Discrimination — Charging different prices to different consumers for the exact same good (e.g., student discounts). Requires market power and inability to resell. Converts consumer surplus into profit.
Negative Externality — Cost spills over to a third party (e.g., pollution). Marginal Social Cost (MSC) > Marginal Private Cost (MPC). Market overproduces. Fix with a per-unit tax.