Question

Show how a firm reaches a general equilibrium of production in a two goods economy with the help of the Edgeworth box diagram.

Short answer

Answer: In a two goods economy, a firm reaches a general equilibrium of production using the Edgeworth box diagram by achieving a state where all producers' marginal rates of transformation (MRTs) are equal, and they have reached their highest possible indifference curve. This state represents a Pareto efficient allocation, at which point no further gains are possible through trade. The general equilibrium is illustrated in the Edgeworth box diagram by finding the point where the indifference curves of both producers sitting on the contract curve are tangent to each other.

Step-by-step solution

Understand the Edgeworth Box Diagram

An Edgeworth box is a graphical representation of a two goods economy, in which one axis represents the quantity of good A and the other axis represents the quantity of good B. The length and width of the box are determined by the total quantities of goods A and B available in the economy. Inside the box, we can illustrate different points representing the various possible production allocations between the two goods.

Define Pareto Efficiency

Pareto efficiency, or optimal allocation, is a state in the Edgeworth box wherein no one's utility can be improved without reducing someone else's utility. In the context of the two goods economy, Pareto efficiency occurs when the marginal rates of transformation (MRTs) for each producer are equal. This is because if the MRTs were not equal, it would be possible to redistribute goods among producers in a way that would benefit at least one party without harming others, thus making the allocation Pareto inefficient.

Introduce Indifference Curves

Indifference curves represent combinations of goods A and B that yield the same level of utility or satisfaction for each producer. In the Edgeworth box, an indifference curve for a producer is drawn as a locus of points representing different allocations of goods A and B at which that producer's utility remains constant.

Outline the Concept of General Equilibrium

A general equilibrium is a state of optimal allocation where all producers' utility functions are adequately satisfied, and no further gains are possible through trade. In a two goods economy, general equilibrium is achieved when all producers' MRTs are equal and producers have reached their highest possible indifference curve. At this point, all goods in the economy are effectively consumed, and there is no room for further reallocation.

Show General Equilibrium in the Edgeworth Box Diagram

To illustrate general equilibrium in the Edgeworth box, start by drawing the box with its dimensions determined by the total amounts of goods A and B. Inside the box, plot some indifference curves for both producers, which should be concave to the origin and convex to the axes. Next, locate the point where the MRTs for both producers are equal, indicating Pareto efficiency. This point is also known as the contract curve and represents the set of all possible Pareto efficient allocations between both producers. The point where the indifference curves of both producers sitting on the contract curve are tangent to each other corresponds to the general equilibrium, indicating that both producers have reached their highest possible indifference curve, and no further gains are possible through trade.