Producer Theory & Existence of equilibrium Assignment

Producer Theory & Existence of equilibrium - Assignment ExampleThere are J producers in an economy. For a producer j, yj represents combination of the quantities of all inputs and outputs. Yj is the set of input and outputs that are technically feasible for the producer j. Without any production in the economy the feasibility instruct would imply that the aggregate consumption (input-output) is not larger than the aggregate endowment. If there is production, then the total resources allocated for consumption increase depending on net outputs of corresponding goods. In Arrow-Debreu model the producers want profit maximization meaning that the input-output combination selected by a firm on a given a price should be such that no other input-output combination gives more profit. We have assumed here that the prices are fixed and firms choose inputs-outputs so as to maximize profit limiting itself to technically feasible combination i.e. yj ? Yj. There are other assumptions that need to be considered for example the one that is often called the tolerant disposal assumption which is- the firm can add any amount of input without reducing output or if we look at it from the cost minimizing plan then it means to add input which can be disposed of at zero cost. If we let p be an original price called by the Walrasian Auctioneer and let yj(p) the associated profit maximizing response.