Economics Edgeworth box

To start with, consider an economy with no production. There are two consumers in the economy. Consumer 1 has an initial endowment of (130, 190) and has an MRS for these two goods of 2y1/x1. Consumer 2 has an initial endowment of (70, 60) and has an MRS for these two goods of y2/x2.

1. Show that P = px/py =1 is not a competitive equilibrium price but P = 2 is. (4 points)

2. Draw an edgeworth box including the endowment, the CE allocation, the IC through the CE allocation, and the budget constraint. Explain why we know the contract curve is not linear. (4 points)

3. Suppose that person 2 is considered more important and should, therefore, have a bigger allocation of the goods. So now the initial endowment of person 2 is (96, 225). Show that the new competitive equilibrium allocation ends up with person 1 having (80, 62.5) and person 2 having (120, 187.5) and show that the new equilibrium price is no longer 2. (6 points) (Note: a picture is not required for credit here, but may be helpful in giving you insight on how to solve the problem)

4. Now there is a change so (200, 250) is just one of many options along a PPF that has a MRT of 5x/2y. Show that now, the outcome in (1) is PE but the outcome in (3) is not. (3 points)

5. Explain why, if there is a negative externality associated with the production of good y, that (1) is no longer PE in the production economy. Explan qualitatively, but not quantitatively how the production of y would be different in a PE allocation than in the allocation in (1).

Economics Edgeworth box

To start with, consider an economy with no production. There are two consumers in the economy. Consumer 1 has an initial endowment of (130, 190) and has an MRS for these two goods of 2y1/x1. Consumer 2 has an initial endowment of (70, 60) and has an MRS for these two goods of y2/x2.

1. Show that P = px/py =1 is not a competitive equilibrium price but P = 2 is. (4 points)

2. Draw an edgeworth box including the endowment, the CE allocation, the IC through the CE allocation, and the budget constraint. Explain why we know the contract curve is not linear. (4 points)

3. Suppose that person 2 is considered more important and should, therefore, have a bigger allocation of the goods. So now the initial endowment of person 2 is (96, 225). Show that the new competitive equilibrium allocation ends up with person 1 having (80, 62.5) and person 2 having (120, 187.5) and show that the new equilibrium price is no longer 2. (6 points) (Note: a picture is not required for credit here, but may be helpful in giving you insight on how to solve the problem)

4. Now there is a change so (200, 250) is just one of many options along a PPF that has a MRT of 5x/2y. Show that now, the outcome in (1) is PE but the outcome in (3) is not. (3 points)

5. Explain why, if there is a negative externality associated with the production of good y, that (1) is no longer PE in the production economy. Explan qualitatively, but not quantitatively how the production of y would be different in a PE allocation than in the allocation in (1).

Economics Edgeworth box

To start with, consider an economy with no production. There are two consumers in the economy. Consumer 1 has an initial endowment of (130, 190) and has an MRS for these two goods of 2y1/x1. Consumer 2 has an initial endowment of (70, 60) and has an MRS for these two goods of y2/x2.

1. Show that P = px/py =1 is not a competitive equilibrium price but P = 2 is. (4 points)

2. Draw an edgeworth box including the endowment, the CE allocation, the IC through the CE allocation, and the budget constraint. Explain why we know the contract curve is not linear. (4 points)

3. Suppose that person 2 is considered more important and should, therefore, have a bigger allocation of the goods. So now the initial endowment of person 2 is (96, 225). Show that the new competitive equilibrium allocation ends up with person 1 having (80, 62.5) and person 2 having (120, 187.5) and show that the new equilibrium price is no longer 2. (6 points) (Note: a picture is not required for credit here, but may be helpful in giving you insight on how to solve the problem)

4. Now there is a change so (200, 250) is just one of many options along a PPF that has a MRT of 5x/2y. Show that now, the outcome in (1) is PE but the outcome in (3) is not. (3 points)

5. Explain why, if there is a negative externality associated with the production of good y, that (1) is no longer PE in the production economy. Explan qualitatively, but not quantitatively how the production of y would be different in a PE allocation than in the allocation in (1).