Question

Consider the general equilibrium of a pure exchange economy in which two agents may engage in trade. The utility functions for the two agents are identical: U¹ = A₁B₁ and U² = A₂ B₂, where A, and B. are consumption levels of the two goods, A and B, for agent i (i = 1, 2). The initial endowment vectors are given as follows: Agent 1: (a₁, b₁)=(0, 100); Agent 2: (a₂, b₂) = (100, 0). Suppose that they both maximize utility and that each agent accepts as given the market price as quoted by a referee.

Calculate the demand functions of both agents.

Answer 1

The demand functions for both agents in the pure exchange economy can be calculated by using the utility-maximizing choice on the consumption budget constraint. The demand functions for both agents are identical and can be represented as A = 50 + 0.5B and B = 50 + 0.5A.

Step-by-step explanation:

The demand functions for both agents in the pure exchange economy can be calculated by using the utility-maximizing choice on the consumption budget constraint. In this case, since the utility functions for both agents are identical, the demand functions for both agents will also be identical.

Let's denote the price of good A as pA and the price of good B as pB. The budget constraint for both agents can be represented as:

pAa1 + pBb1 = pAa2 + pBb2

Solving this budget constraint using the utility maximization rule, we can find the demand functions for both agents as A = 50 + 0.5B and B = 50 + 0.5A.