Private Ownership Economy

Consider a one-producer-one consumer economy (the single agent is both a producer and

a consumer). There are two goods. Good 1 is used as input in the production process.

2Good is output. The aggregate endowment is = (2,0). The consumption set isR+2 .

The production set is described as,

Y= { y R²:y₂ y₁, 0 y₂ 2 } { y R²: 0 y₂ 2, y₁ 2 }

Preferences are represented by u(x₁, x₂) =x₂

1) Find the set of efficient production plans

2) Compute the set of efficient allocations (y, x)

3) Find all the price quasi-equilibrium. Establish whether these are price equilibrium and connect your results with the welfare theorems.

4) Suppose now that = (0,2). Find all the price quasi-equilibrium. Establish whether these are price equilibrium and connect your results with the welfare theorems.