AP Micro Formula Sheet (AP)
What You Need to Know
This is the high-yield AP Micro “formula sheet”: the equations + decision rules you repeatedly use to solve FRQs and multiple choice (elasticity, revenue/cost/profit, market efficiency, taxes/DWL, monopoly vs competition, and factor markets). If you can (1) pick the right formula and (2) apply the right marginal condition, you’re most of the way there.
Core idea you’ll use everywhere:
- Optimize where marginal benefit = marginal cost
- Firm: MR = MC
- Consumer utility: \frac{MU_x}{P_x} = \frac{MU_y}{P_y} (or spend all income on highest MU/P first)
- Hire labor: MRP = MFC
- Efficiency: MSB = MSC
Critical reminder: AP Micro loves “at the margin.” Average values describe; marginals decide.
Step-by-Step Breakdown
1) Elasticity (fast + consistent)
- Identify what elasticity you need (price, income, cross).
- Use the midpoint (arc) method for percent changes (unless clearly “point” changes).
- \%\Delta X = \frac{X_2 - X_1}{(X_1+X_2)/2}
- Plug into elasticity definition.
- For price elasticity of demand, report absolute value (AP convention) unless the sign matters.
Mini-example (midpoint):
- Price rises from \$10 to \$12; quantity falls from 100 to 80.
- \%\Delta Q = \frac{80-100}{(80+100)/2} = \frac{-20}{90} = -0.2222
- \%\Delta P = \frac{12-10}{(12+10)/2} = \frac{2}{11} = 0.1818
- E_d = \left|\frac{-0.2222}{0.1818}\right| \approx 1.22 (elastic)
2) Profit maximization for a firm (any market structure)
- Determine market structure to know how to get MR:
- Perfect competition: MR = P
- Monopoly: MR < P (use MR curve/data)
- Find the output where MR = MC.
- Check shutdown condition (short run):
- Competitive firm shuts down if P < AVC.
- Compute profit:
- \pi = TR - TC where TR = P\cdot Q.
Mini-example (competitive):
- Market price P = 20. Your cost table says at Q=50, MC=20.
- Choose Q=50 (where P=MC), provided P \ge AVC.
- Profit: \pi = (20)(50) - TC(50).
3) Surplus + Deadweight Loss (graphs)
- Find equilibrium (where demand = supply).
- Identify policy wedge (tax, price ceiling/floor) and new quantity.
- Compute areas:
- Triangles: Area = \frac{1}{2}(base)(height)
- Deadweight loss is the lost gains from trade from Q_{efficient} down to Q_{actual}.
Mini-example (per-unit tax):
- Tax t=4, quantity falls from Q^* = 100 to Q_t = 80.
- DWL = \frac{1}{2}(t)(Q^* - Q_t) = \frac{1}{2}(4)(20) = 40.
4) Monopoly from linear demand (quick MR trick)
If demand is linear: P = a - bQ
- Write MR: MR = a - 2bQ
- Set MR = MC to find Q_m.
- Plug Q_m into demand to get P_m.
Key Formulas, Rules & Facts
Elasticity (must-know set)
| Formula / Rule | When to use | Notes |
|---|---|---|
| E_d = \left|\frac{\%\Delta Q_d}{\%\Delta P}\right| | Price elasticity of demand | Use midpoint for changes; report absolute value. |
| \%\Delta X = \frac{X_2 - X_1}{(X_1+X_2)/2} | Midpoint (arc) % change | Prevents different answers depending on direction. |
| E_s = \frac{\%\Delta Q_s}{\%\Delta P} | Price elasticity of supply | Usually positive. |
| E_{income} = \frac{\%\Delta Q}{\%\Delta Y} | Normal vs inferior | E_{income} > 0 normal; E_{income} < 0 inferior. |
| E_{cross} = \frac{\%\Delta Q_x}{\%\Delta P_y} | Substitutes vs complements | >0 substitutes; |
| Total Revenue Test | Elasticity from TR change | If P\uparrow and TR\downarrow, demand is elastic; if TR\uparrow, inelastic; if unchanged, unit elastic. |
Elastic vs inelastic cutoffs:
- Elastic: E_d > 1
- Inelastic: E_d < 1
- Unit elastic: E_d = 1
Revenue, cost, profit (the big 10)
| Formula / Rule | When to use | Notes |
|---|---|---|
| TR = P\cdot Q | Total revenue | For monopoly, P depends on Q from demand. |
| AR = \frac{TR}{Q} | Average revenue | Usually equals price: AR=P. |
| MR = \frac{\Delta TR}{\Delta Q} | Marginal revenue | Competitive: MR=P; Monopoly: MR |
| TC = TFC + TVC | Total cost | TFC constant in short run. |
| AFC = \frac{TFC}{Q} | Average fixed cost | Always decreases as Q increases. |
| AVC = \frac{TVC}{Q} | Avg variable cost | Key for shutdown. |
| ATC = \frac{TC}{Q} = AFC + AVC | Avg total cost | Key for profit vs loss. |
| MC = \frac{\Delta TC}{\Delta Q} = \frac{\Delta TVC}{\Delta Q} | Marginal cost | MC curve crosses AVC and ATC at their minimums (when drawn smoothly). |
| \pi = TR - TC | Profit | Economic profit includes implicit costs. |
| Break-even | When TR=TC | Equivalent: P = ATC at the chosen Q. |
Shutdown vs exit (competitive firm):
- Short run shutdown if P < AVC at profit-maximizing Q.
- Long run exit if P < ATC (cannot cover total costs in the long run).
Production & marginal product links
| Formula / Rule | When to use | Notes |
|---|---|---|
| MP_L = \frac{\Delta Q}{\Delta L} | Marginal product of labor | Diminishing marginal returns: MP_L eventually falls as L rises (short run). |
| Relationship: MC vs MP | Link input productivity to cost | As MP_L\uparrow, MC\downarrow; as MP_L\downarrow, MC\uparrow. |
Market structure decision rules (profit max always looks similar)
| Market | Key condition | Extra notes |
|---|---|---|
| Perfect competition | P = MR = MC | Supply is MC above AVC. Efficient output: P=MC. |
| Monopoly | Choose Q where MR=MC then charge P from demand | Creates DWL: P>MC and output lower than efficient. |
| Monopolistic competition | MR=MC in SR | LR: entry drives \pi \to 0 typically; still P>MC. |
| Oligopoly | No single formula | Often game theory; still “think marginally.” |
Monopoly markup (high-yield relationship):
- \frac{P - MC}{P} = \frac{1}{|E_d|}
- More elastic demand \Rightarrow smaller markup.
Consumer/Producer surplus + efficiency
| Object | How to compute | Notes |
|---|---|---|
| Consumer surplus (CS) | Area under demand above price | Triangle often: CS = \frac{1}{2}(Q)(P_{choke}-P) if linear. |
| Producer surplus (PS) | Area above supply below price | Triangle often: PS = \frac{1}{2}(Q)(P-P_{intercept}) if linear. |
| Total surplus (TS) | TS = CS + PS | Maximized at competitive equilibrium without externalities. |
| Deadweight loss (DWL) | Lost TS from trades not made | Often triangle between S and D over lost quantity. |
Taxes, price controls, and wedges
| Policy | Key quantities | Notes |
|---|---|---|
| Per-unit tax t | Wedge: P_b - P_s = t | Incidence depends on relative elasticities. |
| Tax revenue | TR_{tax} = t\cdot Q_{tax} | Rectangle on graph. |
| DWL of tax | DWL = \frac{1}{2}(t)(Q^* - Q_{tax}) | When supply/demand roughly linear. |
| Binding price ceiling | P_{ceiling} < P^* | Shortage: Q_d > Q_s. |
| Binding price floor | P_{floor} > P^* | Surplus: Q_s > Q_d. |
Incidence rule of thumb:
- The side that is more inelastic bears more of the tax burden.
Externalities (social vs private)
| Concept | Formula | Notes |
|---|---|---|
| Marginal social cost | MSC = MPC + MEC | Negative externality adds external cost. |
| Marginal social benefit | MSB = MPB + MEB | Positive externality adds external benefit. |
| Efficient outcome | MSB = MSC | Social optimum. |
| Pigouvian tax | Set tax per unit \approx MEC at Q_{efficient} | Shifts private incentives to social optimum. |
Factor markets (hiring inputs)
| Formula / Rule | When to use | Notes |
|---|---|---|
| Value of marginal product | VMP = P\cdot MP | When output market is competitive (so MR=P). |
| Marginal revenue product | MRP = MR\cdot MP | General case; if monopoly in output, MR |
| Hire rule | Hire until MRP = MFC | Competitive labor market: MFC = w. |
Examples & Applications
Example 1: Total revenue test (elasticity without calculating)
Demand is inelastic in a price range. If price increases from \$5 to \$6 and total revenue rises from \$500 to \$540:
- P\uparrow and TR\uparrow implies inelastic demand (quantity didn’t fall “enough”).
Example 2: Competitive firm shutdown vs produce-at-a-loss
You find profit-maximizing output where P=MC.
- If P = 8, AVC = 7, ATC = 10 at that Q:
- Produce in the short run (covers variable cost): P \ge AVC.
- But you earn negative profit: P < ATC.
- Loss equals \left(ATC - P\right)Q = (10-8)Q.
Example 3: Monopoly with linear demand (MR shortcut)
Demand: P = 50 - 2Q, marginal cost constant: MC = 10.
- MR = 50 - 4Q
- Set MR=MC: 50 - 4Q = 10 \Rightarrow 4Q = 40 \Rightarrow Q_m = 10
- Price from demand: P_m = 50 - 2(10) = 30
- Profit: \pi = (30)(10) - TC (compute TC using MC and any fixed cost if given).
Example 4: Tax DWL and revenue
A per-unit tax t=2 reduces quantity from Q^*=60 to Q_t=50.
- Tax revenue: TR_{tax} = (2)(50) = 100
- Deadweight loss: DWL = \frac{1}{2}(2)(60-50) = 10
Common Mistakes & Traps
Using endpoint percent change instead of midpoint
- Wrong: \%\Delta Q = \frac{Q_2-Q_1}{Q_1} when AP expects midpoint for discrete changes.
- Fix: Use \frac{Q_2-Q_1}{(Q_1+Q_2)/2} unless explicitly told “point elasticity.”
Forgetting elasticity is usually reported in absolute value
- Wrong: reporting E_d=-1.5 and calling it “inelastic.”
- Fix: Use |E_d| for classification; keep the negative sign only if a question explicitly cares.
Mixing up shutdown and exit conditions
- Wrong: shutting down when P < ATC in the short run.
- Fix: Short run shutdown uses AVC; long run exit uses ATC.
Setting P=ATC to find the profit-maximizing quantity
- Wrong: choosing output where average costs match price.
- Fix: Always pick Q via MR=MC (then evaluate profit using ATC).
Confusing “profit” with “revenue”
- Wrong: concluding “higher price means higher profit.”
- Fix: Profit is TR-TC; price changes can reduce Q and change costs.
Computing DWL with the wrong base or height
- Wrong: using the full equilibrium quantity as the base.
- Fix: DWL triangle base is the quantity reduction \left(Q^*-Q_{new}\right); height is the wedge (tax, external cost/benefit, etc.).
For monopoly, charging the price on the MR curve
- Wrong: finding Q where MR=MC and then using that MR value as price.
- Fix: Use Q_m to read price from the demand curve (AR), not MR.
Tax incidence: assuming “who writes the check” pays
- Wrong: “Producers pay the tax because the law taxes producers.”
- Fix: Economic incidence depends on elasticities; more inelastic side bears more burden.
Memory Aids & Quick Tricks
| Trick / Mnemonic | What it helps you remember | When to use it |
|---|---|---|
| “Midpoint or miss points” | Use midpoint formula for elasticity % changes | Any before/after elasticity calc |
| “MR = MC = max” | Profit-max quantity is where marginals are equal | All firm optimization problems |
| “Shutdown: AVC; Exit: ATC” | Which cost curve matters in SR vs LR | Competitive firm decisions |
| “More inelastic pays more” | Tax burden falls more on inelastic side | Tax incidence questions |
| “Monopoly: MR twice as steep” | For linear demand, MR slope is double demand slope | Quick monopoly math |
| “Social = Private + External” | MSC = MPC + MEC and MSB = MPB + MEB | Externality graphs and policies |
| “Hire where you’re worth what you cost” | MRP = MFC | Factor market input hiring |
Quick Review Checklist
- You can compute percent change with midpoint: \%\Delta X = \frac{X_2-X_1}{(X_1+X_2)/2}.
- You know elasticity types and signs: E_d (absolute value), E_{income} (normal vs inferior), E_{cross} (subs vs comps).
- You can use the total revenue test to classify elasticity without calculating.
- You can write and use: TR=P\cdot Q, \pi=TR-TC, MC=\frac{\Delta TC}{\Delta Q}.
- You always choose output with MR=MC (then check shutdown if competitive).
- Competitive firm rules: supply is MC above AVC; shutdown if P
You’ve got this—if you can pick the right rule and apply it cleanly, AP Micro questions become very mechanical.