# Contract curve for firms with linear utility functions

I am attempting to find a contract curve for a production economy with two linear utility functions.

Normally, I would find the point where the Marginal Rate of Technical Substitution were equal for the two firms. However, in this case, this does not seem to work (I end up getting an equation of two numbers).

How must I proceed?

Is it all places where both functions are equal?

• You have already asked this question, haven't you? May 1 '16 at 9:32
• This is different from that. Both utility functions described for the production economy in this case are linear. May 1 '16 at 9:37

1.) An economy with two agents who both have linear preferences will always have Pareto optimal points along either the right and bottom edges or the left and top edges of the Edgeworth box. Edges are dictated by the ratio of MRSa,MRSb.

2.) The contract curve is the locus of Pareto Optimal points.

• Yes, thank you. Makes sense. Point 1 cleared it up. May 2 '16 at 15:18