DSM-107 Full Course Recap

Session 01

Opportunity cost, economic cost, economic rent

Why growth took off ~250 years ago, and the three-part vocabulary for how anyone decides whether an action is worth it.

The big picture

Growth was flat for millennia, then a "hockey stick" from ~1750 — the Malthusian trap (income gains eaten by population growth) finally broken.
Escape driven by continuous technological progress — the Industrial Revolution, starting in Britain.
Adam Smith (1776) predicted it; Malthus (1798) didn't believe it possible.

Formulas

Net benefit: Benefit − Cost.
Opportunity cost: net benefit of the next-best alternative.
Economic cost: direct cost + opportunity cost.
Economic rent: net benefit − opportunity cost (= Benefit − Economic cost).

Decision rule

Do A if Net benefit(A) > Opportunity cost(A) — equivalently, Benefit(A) > Economic cost(A). The two can never disagree.
Positive rent → do it; zero → indifferent; negative → don't.
Worked numbers (concert vs. babysitting): net benefit €30, opportunity cost €22, economic rent €8.
Both benefit and cost are subjective — rent is person-specific.

A model is a map, not a photograph — it throws away almost everything so the one mechanism you care about stands out.

To measure a subjective benefit or cost: keep raising the price until you'd refuse (that ceiling is your benefit); keep lowering the payment until you'd refuse the deal (that floor is your cost).
Why economic cost isn't accounting cost: a US steel firm had a power contract at $3/unit — cheap on the books. When a power crisis sent the market price to $30/unit, the opportunity cost of burning that power on steel was $30, not $3 — so the firm shut its plant and started reselling power instead. The ledger never would have told them to do that.

Session 02

Comparative advantage & gains from trade

Even a worse-at-everything producer should specialize — in whatever they're least worse at.

Definitions

Absolute advantage: can produce more of a good with the same inputs.
Comparative advantage: lower opportunity cost of that good, relative to the other good.

Greta & Carlos worked numbers

Opportunity cost of 1 ton wheat — Greta 25 apples, Carlos 50 apples.
Lower-cost producer specializes: Greta → wheat, Carlos → apples.
Self-sufficiency total: 800 apples, 44 tons wheat. Specialize + trade: 1,000 apples, 50 tons wheat — bigger pie, both eat more.

Rule to remember

Specialize where your opportunity cost is lowest — not where you're most productive in absolute terms.
Opportunity cost exists even with zero out-of-pocket cost.
Trade price must sit between both parties' opportunity costs for both to gain.

Even if Greta is better than Carlos at growing both crops, she still can't do both at once — the question is never "what am I good at," it's "what do I lose least by doing." She loses less by growing wheat than by growing apples, so wheat is where her time is best spent, full stop.

The feasible trading-price range price = 40 apples/ton

price of 1 ton of wheat, in apples40

both gain — Greta +€225, Carlos +€150 (in apples, on 15 tons traded)

Below 25, Greta loses by selling — she'd rather keep the wheat. Above 50, Carlos loses by buying — he'd rather grow it himself. Only 25–50 works for both.

Session 03

Technology choice & the isocost line

Once engineering-dominated technologies are discarded, only relative input prices decide which one's cheapest.

Formulas

Production function: Y = f(inputs); constant returns to scale: f(λX) = λf(X).
Average product: AP = output ÷ input quantity.
Energy–labour ratio: = slope of the ray from origin = energy intensity.
Isocost line: C = wL + pR; intercepts C/w and C/p; slope −w/p.

Rules

Dominated technology: uses more of both inputs than another for the same output — discard it (the quadrant test), no prices needed.
What's left can only be ranked with input prices.
Proportional change in both input prices → isocost line unchanged. Only relative prices matter.
Only one price changing → isocost line rotates.

The Industrial Revolution story

British wages rose relative to coal price → isocost line steepened.
Switched cost-minimising choice from labour-intensive to energy-intensive technology.
Same output, lower cost → higher profit → innovation rent for the first adopter → Schumpeter's creative destruction.

Why "fixed proportions" — it's cooking. Extra labour with no extra ingredients doesn't make more food; you need both together, in the ratio the recipe calls for. That's why you can't scale one input alone: double the workers with the same machines and coal, and output barely moves.

Which technology is cheapest? wage/coal-price ratio = 0.60

relative wage (w/p) — labour cost vs. coal cost0.60

B (4 workers, 2 tons coal) is cheapest

Three technologies for the same output: A(1 worker, 6 tons coal, energy-intensive), B(4, 2), E(10, 1, labour-intensive). Drag the wage up — cheap labour favours E, expensive labour favours A.

Sessions 04–06

The work–leisure choice

A worker splits the day between paid work and free time, constrained by the wage, guided by preferences. Keynes predicted 15 hrs/week by now; actual is ≈40 — this is the model that explains why.

Vocabulary

endogenous: explained by the model — usually what's on the axes.
exogenous: fixed from outside — the wage; anything not modelled.
ceteris paribus: holding everything else constant.
equilibrium: self-perpetuating outcome, unless an external shock hits.

Formulas

Y = w · H: income from hours worked.
C = w · (24 − t): consumption available, t = free time.
MRT = w: slope of the frontier = opportunity cost of free time.
MRS = |ΔC/ΔT|: slope of the indifference curve, utility held constant.

The optimum & wage rises

MRS = MRT at the tangency — the only equilibrium. MRS > MRT → take more free time; MRS < MRT → cut back.
Budget line pivots on (24, 0) — a wage rise is never a parallel shift on its own.
Parallel shift in a decomposition = income effect; slope change = substitution effect.
Karim, w=€30 → optimum at t=17h, work=7h, C=€210. Keynes predicted 15 hrs/week; actual today ≈ 40 hrs/week, because substitution kept pace with income.

Income line — Y = w · H 7.0 h → €210

hours worked per day (H)7.0

Karim's income is a straight line through the origin. Read backwards, it's also his price for free time: €30 per hour he doesn't work.

preference — what he's willing to trade (MRS)

the market — what he's required to trade (budget line / MRT)

The income line is what the market forces on Karim — it says nothing about what he wants. Indifference curves curve because of a rule the professor kept coming back to all course: the more you already have of something, the less you value one more unit of it.

Diminishing marginal rate of substitution MRS = €30 / hour

drag along the curve — free time (hours)17.0

This is the very curve Karim ends up on. Slide right and the tangent flattens — full belly, cheap next bite:

Around 15 hours, he'd give up ~€84 for one more.
Near 21 hours, barely €9.
At 17 hours, MRS lands on exactly €30 — the same €30 the market charges (next panel).

Feasible set — pivoting on the wage w = €30/hr

hourly wage€30

Test bundle — 12 hours free time, €400 consumption: infeasible at this wage.

MRS = MRT — the tangency MRS €30 · MRT €30

free time chosen (hours)17.0

equilibrium — no reason to move

A raise does two things at once:

Income effect — makes you richer, so you buy more of everything, including free time.
Substitution effect — makes not-working pricier, a kind of FOMO on pay.
It's why a promotion usually buys you less free time, not more — pay goes up, but so does the cost of your time.

Decomposing a wage rise $90 → $130/day

new daily wage (student summer job, was $90)$130

substitution effect dominates — net free time falls

income effect: +14.7 days of free time · substitution effect: −20.9 days · net: −6.3 days

Sessions 07–08

Game theory & social dilemmas

When two or more people's payoffs depend on each other's choices — sometimes self-interest is fine, sometimes it wrecks everyone.

Vocabulary

social dilemma: actions taken independently, in self-interest, produce a socially suboptimal outcome — relative to another outcome that was feasible.
game: players, feasible strategies, information, payoffs.
best response: the strategy giving the highest payoff given the other's choice.
Nash equilibrium: each player's strategy is a best response to the other's.
dominant strategy: best response to every strategy the other might play.

Solving a 2×2 matrix

Row player: tick the higher payoff down each column (holding the other's choice fixed).
Column player: tick the higher payoff across each row.
Cell with two ticks = Nash equilibrium. A game can have more than one — or none in pure strategies.

Two archetypes

Invisible hand (crop game): self-interest → the cell with the highest payoff for everyone.
Prisoners' Dilemma (pest control): dominant-strategy equilibrium gives lower payoffs than a feasible alternative — driven by external effects each player ignores.
Pareto improvement: at least one better off, nobody worse off. Pareto efficient = not dominated by any other allocation. A dominant-strategy equilibrium need not be Pareto efficient.
Fixes: altruism (indifference curves over payoffs turn downward-sloping), repeated interaction (threat of reverting to the bad equilibrium), taxes, institutions.

"A model is a caricature — that's the feature, not the bug." Nobody actually computes payoff matrices before choosing; you learn to play tennis by hand-eye coordination, not equations — but the programmer coding an Xbox tennis game still has to write those equations for the character to behave like a real player would. That's what a game-theory model is doing to your own decisions.
Social dilemma, made concrete: nobody wants to sit in traffic, yet everyone drives — each person counts their own fuel cost and comfort, not the jam they add to everyone else's commute. Same logic behind a group flat's permanently dirty kitchen: cleaning is real effort, everyone hopes someone else does it, so nobody does.

Nash equilibrium finder — edit any payoff matrix Nash equilibrium: —

	Bala: strategy 1	Bala: strategy 2
Anil: strategy 1
Anil: strategy 2

amber number = row player's payoff. teal number = column player's payoff. Type any numbers — best-response ticks and the Nash equilibrium update live.

Tick reading: amber ✓ = row player's best response in that column. teal ✓ = column player's best response in that row. Both ticks in one cell → equilibrium (teal outline).

Sessions 09–10

The firm and its customers

Firms maximise profit subject to the demand curve — the same "willing vs. constrained" logic as the worker's problem, with price and quantity instead of consumption and free time.

Profit & the isoprofit curve

π = (P − C)·Q: TR = P·Q, TC = C·Q.
isoprofit curve: locus of (P, Q) at constant profit; downward-sloping; north-east = higher profit.
demand curve: the firm's constraint; downward-sloping; y-intercept = reservation price.

Scale & cost curves

Returns to scale: Q(λX,λY) =/>/< λQ → CRS / IRS / DRS.
AC = C(Q)/Q = slope of the ray from origin. MC = slope of the total-cost curve.
MC < AC → AC falling; MC > AC → AC rising; they cross at minimum AC = minimum efficient scale.
Class-height trick: if the 30th person joining a room is taller than the room's average, the average rises. Same logic: if the next unit's cost (MC) is above the average so far (AC), average cost rises — below it, average cost falls. That's the whole rule, no calculus needed.

Pricing formulas

MR = P + Q·(dP/dQ): profit-max condition: MR = MC.
isoprofit slope: dP/dQ = −(P−MC)/Q.
elasticity ε: (dQ/Q)/(dP/P) — always negative.
Lerner condition: (P−MC)/P = −1/ε — less price-sensitive customers ⇒ higher margin.

Elasticity, classified

ε = −∞ — perfectly elastic (any price rise, customers leave entirely).
−∞ < ε < −1 — elastic.
ε = −1 — unitary elastic.
−1 < ε < 0 — inelastic.
ε = 0 — perfectly inelastic (price doesn't move quantity at all — e.g. a life-saving medicine).

Price discrimination

1st degree: a different price per person — e.g. pricing by browsing history, or US tuition by parental income.
2nd degree: discount conditional on quantity — "buy one get one," bulk pricing.
3rd degree: pricing by observable group — student discounts, weekday happy hours.

Why margin strategy isn't one-size-fits-all — same theory, opposite strategies, both rational, because elasticity differs, not competence:

Tesco: "pile it high, sell it cheap" — ~6.5% margin, profit from volume, flat demand curve (customers have little willingness to pay above cost).
Apple: prices at a premium — ~50–58% margin on iPhones, profit per unit, steep demand curve (loyal customers, high willingness to pay).

Price, elasticity, and the profit-maximising margin P = $5.00

price charged$5.00

margin below what elasticity allows — raise price

Q=19,000 · ε=−0.79 (inelastic) · actual margin (P−MC)/P = 0.60 · elasticity-implied margin −1/ε = 1.27