7.2 Edgeworth box and contract curve

The Edgeworth box is a powerful tool for visualizing resource allocation between two people. It shows how they can trade goods to reach efficient outcomes where both are better off. This concept is key to understanding how markets work and why trade benefits everyone involved.

The contract curve within the Edgeworth box represents all possible efficient allocations. It helps economists analyze trade-offs between fairness and efficiency, showing how different starting points lead to different outcomes. This ties into broader ideas about market equilibrium and economic welfare.

Resource allocation in an Edgeworth box

Structure and components of the Edgeworth box

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• Edgeworth box graphically represents allocation of two goods between two individuals in a pure exchange economy
• Dimensions of the box represent total quantities of two goods available (bananas, apples)
• Box combines two individuals' indifference maps
  • One individual's preferences represented from bottom-left origin
  • Other individual's preferences represented from top-right origin
• Each point within box represents specific allocation of two goods between individuals
• Indifference curves for both individuals plotted within box
  • Slopes of curves represent marginal rates of substitution (MRS) between goods

Analyzing allocations and trades

• Box allows visualization of initial endowments, potential trades, and efficient allocations
• Tangency points of indifference curves from both individuals represent potential efficient allocations
  • MRS equal at these points
• Movements within box represent potential trades between individuals
• Lens formed by indifference curves passing through initial endowment point
  • Allocations outside lens not individually rational
  • Will not be accepted by both parties

Contract curve and its significance

Definition and characteristics

• Contract curve connects set of all Pareto efficient allocations within Edgeworth box
• Points on curve represent allocations where MRS for both individuals equal for both goods
• Curve connects tangency points of indifference curves from one corner of box to opposite corner
• Shape and position of curve depend on preferences of both individuals
  • Represented by their indifference curves

Importance in economic analysis

• Crucial for determining set of possible efficient outcomes in bilateral bargaining and exchange
• Helps policymakers and economists understand range of efficient allocations possible in economy
• Any movement along curve benefits one individual while harming other
  • Impossible to improve one person's welfare without reducing other's
• Used to analyze trade-offs between equity and efficiency in resource allocation

Efficiency of allocations in the Edgeworth box

Types of allocations

• Efficient allocations lie on contract curve
  • Indifference curves of both individuals tangent
  • MRS equal
• Inefficient allocations represented by points not on contract curve
  • Potential for mutually beneficial trade exists
• Pareto improvements involve movements from inefficient allocation towards contract curve
  • At least one individual's welfare increases without decreasing other's

Analyzing allocation efficiency

• Core of Edgeworth box represents set of allocations that cannot be improved upon by any coalition
• Efficiency of allocations assessed by examining distance from contract curve
• Potential for mutually beneficial trades indicates inefficiency
• Allocations outside lens formed by indifference curves passing through initial endowment not individually rational
  • Will not be accepted by both parties

Contract curve vs Pareto efficiency

Relationship between contract curve and Pareto efficiency

• Contract curve represents set of all Pareto efficient allocations in Edgeworth box
• Every point on curve satisfies Pareto efficiency condition
  • MRS for both individuals equal
• Moving from point not on curve to point on curve represents Pareto improvement
  • Increases at least one individual's utility without decreasing other's

Economic theorems and implications

• First Fundamental Theorem of Welfare Economics
  • Any competitive equilibrium leads to Pareto efficient allocation
  • Corresponds to point on contract curve
• Second Fundamental Theorem of Welfare Economics
  • Any Pareto efficient allocation on curve achievable through competitive market
  • Requires appropriate initial endowments
• Analyzing curve helps understand how different initial endowments and preferences lead to various Pareto efficient outcomes
• Shape of curve illustrates range of possible efficient allocations
  • Highlights trade-offs between equity and efficiency in resource allocation