Chapter 15: Problem 2

The general equilibrium of production in a two goods economy can be depicted with the help of the Edgeworth box diagram.

Short Answer

Expert verified

Answer: The general equilibrium of production in a two goods economy using the Edgeworth box diagram is the point where both producers are efficiently using their resources and producing the optimal combination of the two goods according to their production functions. This is represented by the intersection of the two Production Possibility Frontier (PPF) curves within the Edgeworth box, indicating the optimal allocation of resources between the two producers and the two goods under specific production functions and resource constraints.

Step by step solution

Understanding the Edgeworth Box

The Edgeworth box is a graphical representation of a two goods economy, with the width and height of the box representing the total resources available for production. Each axis represents one of the goods, with the origin for Producer 1 in the bottom left corner and the origin for Producer 2 in the top right corner.

Defining the Production Possibility Frontier

The Production Possibility Frontier (PPF) is a curve that shows the maximum amount of one good that can be produced given a certain amount of the other good, assuming efficient use of resources. In the Edgeworth box, the PPF will be represented as two curves: one for Producer 1, with its PPF starting from the bottom left corner, and another for Producer 2, with its PPF starting from the top right corner. The shape of each PPF will depend on the specific production technology and resource constraints for each producer.

Plotting the PPFs in the Edgeworth Box

To plot the PPFs, we first need to determine the resource constraints and production functions for each producer. Once we have that information, we can draw the PPF curves in the Edgeworth box. In general, the PPF will be a downward-sloping curve for Producer 1, starting from the bottom left corner, and a downward-sloping curve for Producer 2, starting from the top right corner. The shape of the curves will depend on the specific production functions and resource constraints.

Finding the Equilibrium Point

The general equilibrium of production occurs when both producers are producing at a level where they are maximizing their utility, given the constraints they face. In the Edgeworth box, this corresponds to a point where the two PPF curves intersect. At this point, both producers are efficiently using their resources and producing the optimal combination of the two goods according to their production functions. To find the equilibrium point, look for the point where the two PPF curves intersect.

Analyzing the General Equilibrium

Once the equilibrium point has been identified, we can analyze the general equilibrium of production in the two goods economy. This point will represent the optimal allocation of resources between the two producers and the two goods. This equilibrium point shows that both producers are using their resources efficiently, and no further gains can be made by reallocating resources between the two producers. The equilibrium point also indicates the optimal production levels for each good given the current resource constraints and production technologies.