Economics

1)

a) Show an Edgeworth box for a general case of two agents who both have Cobb-Douglas preferences. (Make sure to label axis and curves.)

b) Briefly explain what the contract curve is.

2) For two agents, a and b, with the following utility functions over goods x and y

a) Determine the slope of the contract curve in the interior of an Edgeworth box that would show this two-person two-goods situation.

b) For initial endowments ωa=(12,7) and ωb=(9,10), what is the Walras allocation between the two agents a and b? (Remember that it is the relative price of the goods that matters in this consideration. Also remember that all the units of goods that exist here are will end up with one or the other agent; so, the overall 21 units of x and the 17 units of y will be fully allocated between the two. )

c) Calculate the utility level before and after trading.

3) For two agents, a and b, with the following utility functions over goods x and y

a) Determine the slope of the contract curve in the interior of an Edgeworth box that would show this two-person two-goods situation.

b) For initial endowments ωa=(9,8) and ωb=(6,7), what is the Walras allocation between the two agents a and b?

c) Calculate the utility level before and after trading.

4) For two agents, a and b, with the following utility functions over goods x and y

a) Determine the slope of the contract curve in the interior of an Edgeworth box that would show this two-person two-goods situation.

b) For initial endowments ωa=(4,5) and ωb=(3,2), what is the Walras allocation between the two agents a and b? (Remember that it is the relative price of the goods that matters in this consideration.)

c) Calculate the utility level before and after trading.