Edgeworth Box

• Contract Curve is the set of pareto efficient points in the edgeworth box.
  • Example. The black curve in (b) is the contract curve.
  • The gradient of the two curves must be equal in every point of the contract curve.
  • The Core is the set of Pareto efficient allocations that make both parties better off than their endowments. (The highlighted section inside the green is the core.)
• Equilibrium is when the exchange rate of goods (i.e. the price ratio) is set in such a way that trade occurs and there is market clearance (i.e. $Q_{\text{demand}}=Q_{\text{supply}}$).
  • It must be pareto efficient.
  • Example of a Disequilibirum. Here. price is set to $1\text{ orange}=1\text{banana}$. Blue player will move $E_1\to A$, and red $E_2\to B$. But those two points do not meet.
  • Example of Equilibirum. Here, price is set to $1.5\text{orange}=1\text{banana}$. Blue moves $E\to C$, and Pink moves $E\to C$ and therefore demand for bananas is equal to supply of bananas, and demand for oranges are equal to supply of oranges.
  • Solving for the equilibirum:
    1. Get the Ordinary Demand for good $x_1$ from both parties.
       • in this case, the Budget Constraint is $I=p_1{e}_1+p_2{e}_2$
    2. Set the equilibirum condition $Q_{\text{demand}}=Q_{\text{supply}}$
       • $x_1^A+x_1^B=e_1^A+e_1^B$
       • $\text{Demand by A}+\text{Demand by B}=\text{Endowment of A}+\text{Endowment of B}$
    3. Solving this for the price ratio $\frac{p_1}{p_2}$ will yield the relative price (=price that will lead to a trade that results in an equilibirum).