Question

In: Economics

Prove that that contract curve will be a straight line if the utility function for both...

Prove that that contract curve will be a straight line if the utility function for both consumers is U=3x²_iy_i

Expert Solution

The pareto-optimal allocations would be where . For the consumer A, we have the utility as , and the marginal rate of substitution would be as or or or or or . It can be also found as , which would yield the same result.

For consumer B too, we have the same utility as , and the marginal rate of substitution would be as or or or or or .

The pareto-optimal allocation in this case would hence be where or or . The feasibility conditions are and or and , where and are the (given) endowments of A and B.

Putting this to the pareto-optimal condition, we have or or or or , which is the contract curve, and is an equation of straight line through the origin.

Rahul Sunny answered 1 year ago

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