Derive the excess demand function z(p) for the economy, for example:

Let us take a simple two-person economy and solve for a Walrasian equilibrium. Let consumers 1 and 2 have identical CES utility functions,

u_i(x₁,x₂)=x₁+x₂,i=1,2,where 0< <1. Let there be 1 unit of each good and suppose each consumer owns allof one good, so initial endowments are e¹=(1,0)and e²=(0,1). Because the aggregateendowment of each good is strictly positive and the CES form of utility is strongly increasingand strictly quasiconcave onRⁿ₊when 0< <1

In addition, find all the Pareto ecient allocations of the economy. Which of them are in the core of the economy?

CES: constant elasticity of substitution

the example is from the text book "advanced microeconomic theory" by Philip J. Reny, 3rd edition, example 5.1