Two agents meet to trade two goods. Agent 1 has preferences representable by utility func- tion...

Transcribed Image Text:

Two agents meet to trade two goods. Agent 1 has preferences representable by utility func- tion u (x()) = x() (x()), while agent 2's preferences are representable by utility function u (x(2)) (x(2)) 3x(2). Agent 1 brings 1 unit of each good to trade, while agent 2 brings 2 = units of each good. 1. Find the set of all Pareto-efficient allocations. Plot it in an Edgeworth box. 2. Calculate the slope of each agent's indifference curve through their endowment. Are the indifference curves tangent? What does this tell you about whether the endowments are Pareto-optimal? 3. On the same diagram, plot the endowment and each agent's indifferent curve through it. 4. On the same diagram, shade in the set of Pareto improvements over the endowment. 5. On the same diagram, identify the contract curve. 6. Find a Pareto-optimal allocation which satisfies voluntary participation. (Hint: Use your diagram to choose a feasible value for x(), and then use your answer to part 1 to back out the rest of the allocation. Make sure to check that the allocation you've found is a Pareto improvement.) Two agents meet to trade two goods. Agent 1 has preferences representable by utility func- tion u (x()) = x() (x()), while agent 2's preferences are representable by utility function u (x(2)) (x(2)) 3x(2). Agent 1 brings 1 unit of each good to trade, while agent 2 brings 2 = units of each good. 1. Find the set of all Pareto-efficient allocations. Plot it in an Edgeworth box. 2. Calculate the slope of each agent's indifference curve through their endowment. Are the indifference curves tangent? What does this tell you about whether the endowments are Pareto-optimal? 3. On the same diagram, plot the endowment and each agent's indifferent curve through it. 4. On the same diagram, shade in the set of Pareto improvements over the endowment. 5. On the same diagram, identify the contract curve. 6. Find a Pareto-optimal allocation which satisfies voluntary participation. (Hint: Use your diagram to choose a feasible value for x(), and then use your answer to part 1 to back out the rest of the allocation. Make sure to check that the allocation you've found is a Pareto improvement.)