Imagine we have an economy with two agents, Anna and Brad, and two goods: participation trophies...

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Imagine we have an economy with two agents, Anna and Brad, and two goods: participation trophies (X) and craft beers (Y).¹ Anna's utility is given by U=XA YA and Brad's is given by Und Xs+Ys. Anna's MRS is MRSAA and Brad's MRS of X for Y is 1. Brad is a simple guy, I guess. Finally, suppose Anna begins with 4 of good X and 2 of good Y, while Brad begins with 2 of good X and 3 of good Y. There is no production so we're stuck with this amount of X and Y but not with this distribution. First Welfare Theorem 1. Draw the Edgeworth Box for this economy. Include the initial endowment point and the indifference curves that pass through this point for each consumer. Your indifference curves don't need to be artistic but if the curves are curvy they should look like that while if they are straight lines they should be straight. 2. Find the conditions characterizing the Pareto efficient set. Graph this set on the Edgeworth box. (Hint: Don't forget to also use the constraint that there is no production. What does that mean about the total amount of X, e.g. X₁ + Xs?) 3. Mark the boundary points of the "Contract Curve" - ie the part of the Pareto Efficient set that both Anna and Brad weakly prefer to the initial endowment. 4. Set the price of X (Px) equal to 1. Find the price of Y in equilibrium (Hint: set both MRS = Px/Pr. the price ratio). 5. Using these prices, and the budget constraint implied by the initial endowment, find the competitive equilibrium Pareto efficient allocation of X and Y. Second Welfare Theorem Suppose Anna is a jerk. We want here utility to be U=1 which is easy to achieve if XAYA 1. 6. You can ensure Anna gets that allocation by taking some of her endowment as a tax. How many units of good X do you need to take from her as a tax. Imagine we have an economy with two agents, Anna and Brad, and two goods: participation trophies (X) and craft beers (Y).¹ Anna's utility is given by U=XA YA and Brad's is given by Und Xs+Ys. Anna's MRS is MRSAA and Brad's MRS of X for Y is 1. Brad is a simple guy, I guess. Finally, suppose Anna begins with 4 of good X and 2 of good Y, while Brad begins with 2 of good X and 3 of good Y. There is no production so we're stuck with this amount of X and Y but not with this distribution. First Welfare Theorem 1. Draw the Edgeworth Box for this economy. Include the initial endowment point and the indifference curves that pass through this point for each consumer. Your indifference curves don't need to be artistic but if the curves are curvy they should look like that while if they are straight lines they should be straight. 2. Find the conditions characterizing the Pareto efficient set. Graph this set on the Edgeworth box. (Hint: Don't forget to also use the constraint that there is no production. What does that mean about the total amount of X, e.g. X₁ + Xs?) 3. Mark the boundary points of the "Contract Curve" - ie the part of the Pareto Efficient set that both Anna and Brad weakly prefer to the initial endowment. 4. Set the price of X (Px) equal to 1. Find the price of Y in equilibrium (Hint: set both MRS = Px/Pr. the price ratio). 5. Using these prices, and the budget constraint implied by the initial endowment, find the competitive equilibrium Pareto efficient allocation of X and Y. Second Welfare Theorem Suppose Anna is a jerk. We want here utility to be U=1 which is easy to achieve if XAYA 1. 6. You can ensure Anna gets that allocation by taking some of her endowment as a tax. How many units of good X do you need to take from her as a tax.

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First Welfare Theorem 1 The Edgeworth box for this economy is shown below The initial endowment point is marked with an E The indifference curves that ... View the full answer