Generated by AskSia.ai — graphs, formulas, traps
Budget: P_x · X + P_y · Y = I Slope of BL = −P_x / P_yIncome increase → BL shifts parallel outward. Price change → pivots the BL (one intercept moves).
MU_x / P_x = MU_y / P_y ⇔ MRS = P_x / P_yThe 'last dollar spent' should give the same marginal utility on each good. If MU_x/P_x > MU_y/P_y, buy more X.
| Concept | Definition |
|---|---|
| MU (marginal utility) | extra utility from one more unit |
| Diminishing MU | each extra unit gives less |
| MRS | −ΔY/ΔX along indifference curve |
| Substitution effect | switch toward cheaper good (along IC) |
| Income effect | real income changes with prices |
Slutsky decomposition: total price-change effect = substitution + income. Sub effect always ≤ 0 (along IC). Income effect's sign depends on normal/inferior.
Tangency MRS = P_x/P_y assumes interior solution. If a good's MU/P is way bigger at every quantity, you spend everything on it (corner solution). Always check corners — graders deduct for missing them.
Private market sets MB = MC. Social cost includes external harm: MSC > MPC. Market equilibrium produces too much at price too low.
Pigouvian tax = marginal external cost → internalizes the externalityMSB > MPB. Market produces too little. Solution: subsidy = marginal external benefit.
| Externality | Effect | Fix |
|---|---|---|
| Negative production | Q_market > Q_efficient | tax = MEC |
| Positive consumption | Q_market < Q_efficient | subsidy = MEB |
| Common-pool | tragedy of the commons | property rights / quotas |
Public-goods classification: Rival + Excludable = private. Non-rival + Excludable = club good. Rival + Non-excludable = common-pool. Non-rival + Non-excludable = pure public good.
Positive externality means the market under-produces the good. The fix is a subsidy, not a tax. Many students confuse 'externality' with 'something to discourage' and apply tax universally. Direction matters.
Q = f(L, K) MP_L = ∂Q/∂L, MP_K = ∂Q/∂KReturns to scale: scaling all inputs by t. Q(tL, tK) compared to tQ. Constant (CRS) = same. Increasing (IRS) > tQ. Decreasing (DRS) < tQ.
| Cost | Formula | Note |
|---|---|---|
| TC | FC + VC | FC fixed in SR |
| AFC | FC/Q | falls continuously |
| AVC | VC/Q | U-shaped |
| ATC | TC/Q | U-shaped |
| MC | ΔTC/ΔQ | cuts AVC, ATC at minima |
LR cost minimization: MP_L / w = MP_K / r ⇔ MRTS = w/rMR = MC. For perfect comp: P = MR. For monopoly: MR < P. Then check shutdown.Shutdown: short run, produce if P ≥ AVC (covers variable cost, FC sunk). Long run, exit if P < ATC.
Short-run shutdown threshold is AVC (FC is sunk, can't be avoided). Long-run exit threshold is ATC (all costs avoidable). Mixing the two is the most-deducted firm-theory mistake.
Players choose strategies; payoffs depend on others' choices. Nash equilibrium: each player's strategy is a best response to others' — no one wants to deviate unilaterally.
| B Cooperate | B Defect | |
|---|---|---|
| A Cooperate | (−1, −1) | (−10, 0) |
| A Defect | (0, −10) | (−5, −5) |
Each player's dominant strategy is Defect (better regardless of opponent). Nash eq = both defect = (−5, −5). Cooperative outcome (−1, −1) is unreachable without binding agreement. Tragedy of unilateral incentives.
Repeated games: finite horizon → backward induction → defect every round. Infinite horizon → cooperation sustainable via tit-for-tat or grim trigger if discount factor δ high enough.
Mixed strategies: assign probabilities to make opponent indifferentA dominant strategy is best regardless of others. A dominated strategy is worst regardless. They're opposites — don't confuse. To find Nash, eliminate dominated strategies first; if dominant exists for both, that's the unique Nash.
VMP_L = P · MP_L (value of marginal product, perfectly competitive output)MRP_L = MR · MP_L (marginal revenue product, more general)Firm hires labor up to where w = MRP_L. Demand for labor is the MRP curve.
| Effect of higher w | Effect on hours |
|---|---|
| Substitution effect | more work (leisure costlier) |
| Income effect | less work (richer, can afford leisure) |
| Net | typically + at low w, − at high w → backward-bending |
Human capital: investments (education, training) raise productivity → MRP up → wages up. Explains education-wage premium without invoking magic.
In perfectly competitive labor market, min wage above eq creates unemployment (textbook). In monopsony, well-set min wage can increase employment by forcing the employer to hire to the competitive level. Don't apply one rule everywhere.
Profit-max: P = MR = MC Shutdown if P < AVC (SR), exit if P < ATC (LR)Competitive firm is a price taker. Demand curve facing the firm is horizontal at market P. Firm chooses Q where MC crosses P from below.
| Stage | Outcome |
|---|---|
| SR profit (P > ATC) | entry → S shifts right → P falls |
| SR loss (P < ATC) | exit → S shifts left → P rises |
| LR equilibrium | P = min ATC, zero economic profit |
Tax incidence: burden falls on inelastic side. Perfectly inelastic D → consumers pay all. Perfectly elastic S → consumers pay all (firms can't absorb).
'Zero economic profit' in long-run perfect competition means firms earn normal accounting profit (covers opportunity cost). Doesn't mean accountants see $0. Many students think it means firms close — they don't. They earn just enough to stay.
| Structure | Firms | Product | Entry | P vs MC |
|---|---|---|---|---|
| Perfect comp | many | identical | easy | P = MC |
| Monop comp | many | differentiated | easy | P > MC slightly |
| Oligopoly | few | similar/diff | blocked | P > MC, strategic |
| Monopoly | 1 | unique | blocked | P >> MC |
MR drops twice as fast as D (linear): MR = a − 2bQ when D: P = a − bQMonopolist: produces where MR = MC, then reads P from demand curve. Compared to competitive: lower Q, higher P, deadweight loss.
Lerner index: (P − MC)/P measures market power. 0 in perfect comp, → 1 for unconstrained monopoly.
For monopoly, DON'T set demand = MC. Quantity comes from MR = MC; only then go up to D for the price. The vertical distance between MR and D is the source of market power.
| Question says… | Use § from | Move |
|---|---|---|
| 'budget line', 'income / price change' | § ① | BL pivot vs shift; new optimum tangent |
| 'utility max', MU/P | § ① | set MU_x/P_x = MU_y/P_y; corner check |
| 'normal vs inferior' | § ① | income effect direction |
| 'isoquant', cost-min | § ② | tangent: MRTS = w/r |
| 'shutdown' / 'exit' | § ② | SR: P vs AVC; LR: P vs ATC |
| 'returns to scale' | § ② | Q(tL,tK) vs tQ — long run |
| 'long-run equilibrium', perfect comp | § ③ | P = min ATC, zero economic profit |
| 'tax incidence' | § ③ | burden falls on inelastic side |
| 'consumer surplus / DWL' | § ③ | area between D, S, P |
| 'monopoly Q and P' | § ④ | MR = MC for Q, then read P off D |
| 'price discrimination' | § ④ | 1st/2nd/3rd degree distinction |
| 'natural monopoly regulation' | § ④ | P = MC (loss) or P = ATC (efficient breakeven) |
| 'Cournot duopoly' | § ⑤ | best-response in Q, find Nash intersection |
| 'Bertrand duopoly' | § ⑤ | P → MC if identical products |
| prisoner's dilemma / Nash | § ⑤ | dominant strategy → both 'defect' → suboptimal |
| 'externality, tax/subsidy' | § ⑥ | negative → tax = MEC; positive → subsidy = MEB |
| 'Coase theorem' | § ⑥ | private bargaining → efficient if T-costs low |
| 'public good', 'free rider' | § ⑥ | non-rival + non-excludable → market under-provides |
| 'wage = ?', labor demand | § ⑦ | w = MRP_L = MR · MP_L |
| 'min wage effect' | § ⑦ | depends on market: comp vs monopsony |
Micro questions reward graph-based thinking. Drawing D, S, MR, MC with shifts and shaded areas is worth 30-50% of the points. Even if numerical answer is wrong, a correct diagram earns partial credit. Words alone won't.
Quantities have units. Prices in dollars. DWL is a dollar area. Direction of shift matters: 'demand falls' → D shifts LEFT, not down. Be precise about what changes and what stays.