Question

Suppose there are two goods, X and Y, and many identical consumers. Production exhibits increasing costs.

(A) Illustrate and explan why Pareto efficiency requires that the marginal rate of transformation between the two goods equal the marginal rate of substitution.

(B)explain why the competitive equilibrium is a Pareto optimum.

(C) suppose now that the government taxes consumption of good X so that the price paid by consumers rises to Px(1+tx).Compare and Illustrate the equilibrium for this case relative to the competitive equilibrium.

Answer 1

A. The two main conditions of Pareto optimality are: 1. Efficiency in Exchange 2. Efficiency in Production.

1. Efficiency in Exchange:

The required condition is that “the marginal rate of substitution between any two products must be the same for every individual who consumes both.”

It means that the marginal rate of substitution (MRS) between two consumer goods must be equal to the ratio of their prices. Since under perfect competition every consumer aims at maximising his utility, he will equate his MRS for two goods, X and Y to their price ratio (Px/Py).

2. Efficiency in Production:

The required condition is that the marginal rate of technical substitution (MRTS) between any two factors must be the same for any two firms using these factors to produce the same product.

In fact, the MRT of X for Y is equal to the ratio of the marginal cost of product X (MCX) to that of product Y (MCX). But each firm produces that level of output at which its marginal cost is equal to its market price. Therefore, for each firm Px = MCX and Py = MCY Hence MCX/MCY = PX/Py.

Efficiency in Exchange and Production (Product Mix):

Pareto optimality under perfect competition also requires that the marginal rate of substitution (MRS) between two products must equal the marginal rate of transformation (MRT) between them. It means simultaneous efficiency in consumption and production.

Since the price ratios of the two products to consumers and firms are the same under perfect competition, the MRS of all individuals will be identical with MRT of all firms consequently, the two products will be produced and exchanged efficiently. Symbolically, MRSXY = PX/PY, and MRTxy = Px/Py. Therefore, MRSXY = MRTxy.