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)

1. Identify what elasticity you need (price, income, cross).
2. Use the midpoint (arc) method for percent changes (unless clearly “point” changes).
   • $\%\Delta X = \frac{X_2 - X_1}{(X_1+X_2)/2}$
3. Plug into elasticity definition.
4. 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)

1. Determine market structure to know how to get $MR$:
   • Perfect competition: $MR = P$
   • Monopoly: $MR < P$ (use MR curve/data)
2. Find the output where $MR = MC$.
3. Check shutdown condition (short run):
   • Competitive firm shuts down if $P < AVC$.
4. 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)

1. Find equilibrium (where demand = supply).
2. Identify policy wedge (tax, price ceiling/floor) and new quantity.
3. Compute areas:
   • Triangles: $Area = \frac{1}{2}(base)(height)$
4. 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: $P = a - bQ$

1. Write MR: $MR = a - 2bQ$
2. Set $MR = MC$ to find $Q_m$.
3. Plug $Q_m$ into demand to get $P_m$.

Key Formulas, Rules & Facts

Elasticity (must-know set)

Elastic vs inelastic cutoffs:

• Elastic: $E_d > 1$
• Inelastic: $E_d < 1$
• Unit elastic: $E_d = 1$

Revenue, cost, profit (the big 10)

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

Market structure decision rules (profit max always looks similar)

Monopoly markup (high-yield relationship):

• $\frac{P - MC}{P} = \frac{1}{|E_d|}$
• More elastic demand $\Rightarrow$ smaller markup.

Consumer/Producer surplus + efficiency

Taxes, price controls, and wedges

Incidence rule of thumb:

• The side that is more inelastic bears more of the tax burden.

Externalities (social vs private)

Factor markets (hiring inputs)

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

1. 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.”

2. 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.

3. 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 $ATC$.

4. 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 $ATC$).

5. Confusing “profit” with “revenue”

   • Wrong: concluding “higher price means higher profit.”
   • Fix: Profit is $TR-TC$; price changes can reduce $Q$ and change costs.

6. 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.).

7. 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.

8. 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

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 $P<AVC$; exit in LR if $P<ATC$.
• You can compute CS/PS/DWL as triangle areas: $\frac{1}{2}(base)(height)$.
• For per-unit tax: wedge $P_b-P_s=t$, revenue $t\cdot Q_t$, DWL $\frac{1}{2}(t)(Q^*-Q_t)$.
• Monopoly with linear demand: if $P=a-bQ$ then $MR=a-2bQ$.
• Externalities: efficient where $MSB=MSC$; use Pigouvian tax/subsidy to internalize.

You’ve got this—if you can pick the right rule and apply it cleanly, AP Micro questions become very mechanical.