Pure Exchange Model: Indifference Curves, Endowments, Edgeworth Box, and Terms of Trade

Pure Exchange Model: Key Assumptions

  • Two individuals: Smith and Jones

  • Goods: apples (A) and oranges (O); homogeneous

  • Preferences: more is better; diminishing marginal utility

  • Utility measured in utils; can rank bundles, even if exact numbers are not comparable across people

  • Endowments: ES = (O,A) = (10,0), \, EJ = (O,A) = (0,10)

  • Trade: mutually voluntary; individuals maximize utility; perfect knowledge of goods and quality

  • Edgeworth box represents total resources: O{total}=10,\ A{total}=10

  • Implicit vs explicit assumptions noted; later relaxations allow for intermediation, communication, etc.

Indifference Curves: Visualization and Rules

  • Indifference curve: all allocations giving same utility

  • More is better ⇒ curves located up and to the right; higher curves imply higher utility

  • Curves are bowed toward the origin due to diminishing marginal utility

  • Endowment point lies on the box; moving to other points shows possible trade outcomes

  • Terms: bundle, allocation refer to a specific point on the graph

Endowments and Edgeworth Box

  • Edgeworth box dimensions equal total goods: O{total}=10,\ A{total}=10

  • Endowment points within the box: Smith at ES=(10,0); Jones at EJ=(0,10)

  • Overlay of both individuals’ indifference curves on the box shows all feasible allocations

  • Trade is represented by moving along diagonals (exchange) within the box

Trade: The Lens and Gains from Exchange

  • The region between the two individuals’ indifference curves through the endowment forms a lens (eye-shape)

  • Moving from endowment to a point in the lens makes both better off (mutual gains)

  • Intuition: diminishing marginal utility means the first few units of the new good are highly valued; e.g., Smith prefers first apple over his tenth orange

  • One-for-one trade can be sufficient to improve both, moving to higher indifference curves

  • Surplus value: additional welfare from trade not captured by simple dollar-value measures of goods; trade can increase total welfare beyond initial endowment

Terms of Trade (TOT) and Prices

  • TOT expresses the rate of exchange between goods: ext{TOT} = rac{pO}{pA}

  • Units: apples per orange (or its reciprocal: oranges per apple)

  • If asked for TOT in terms of PO/PA, ensure it corresponds to the intended direction (apples per orange vs oranges per apple)

  • Example: moving from endowment e to a one-for-one trade yields ext{TOT} = 1 (one orange per one apple)

Why Trade Happens: Intuition and Welfare

  • With more is better and diminishing MU, endowments differ, creating opportunities for mutually beneficial trades

  • The lens shows allocations where both agents achieve higher utility than at the endowment

  • If trade occurs and is voluntary, both parties can be better off; non-selfish motives are not required for gains

Quick Reference Points

  • Edgeworth box captures all feasible allocations for two agents with fixed totals

  • Endowments determine the starting point for potential gains from trade

  • Intermediaries (e.g., information channels) can affect reachability, but the basic lens concept remains core

  • Key takeaway: under the basic assumptions, trade is win-win and creates surplus value beyond simple dollar-value measures