1)Recall Abe and Betty from the Wissink web-workbook problem set PS99 Q2. That is, suppose uAbe=min{2F, IC} and uBetty=min {1F, 1C}. Assume total food available is F=100 and total clothing available is C=50.
a)What allocations of food and clothing are on the "contract curve" in the Edgeworth-box for Abe and Betty?
b)What allocations of food and clothing are on the "core" in the Edgeworth-box for Abe and Betty?
c)Transcribe the allocations in your Edgeworth Box into a detailed utility possibilities frontier diagram.
d)Suppose now that we agree that social welfare should be measured with the following function: Wsociety=utilityAbe + utilityBetty . What allocation/allocations on your utility possibilities frontier in part (c) would maximize this social objective function?
e)Suppose now that we agree that social welfare should be measured with the following function: Wsociety=min{utilityAbe , utilityBetty }. What allocation/allocations on your utility possibilities frontier in part (c) would maximize this social objective function?
2)Suppose Abe and Betty are in a pure exchange economy with no production. They have identical utility functions over the only two goods in their world beer (B) and ribs (R) as follows: uabe=BARA and ubetty=BBRB. Suppose the following initial endowment situation: Abe’s has 1unit of ribs and 4 units of beer; Betty has 5 units of ribs and 8 units of beer.
a)PUTTING RIBS ON THE HORIZONTAL and BEER ON THE VERTICAL, illustrate the status quo situation at hand in a carefully drawn Edgeworth/Bowley box. Put Abe in the lower left and Betty in the upper right.
b)Given these utility functions, what is the general expression for Abe’s MRS in terms of any beer and ribs bundle he consumes? What is it for Betty?
c)At any interior Pareto Efficient allocation, what must be the relationship between Abe’s ribs and beer bundle relative to Betty’s ribs and beer bundle?
d)In your box, find the locus of points where the condition above will be true, given the dimensions of the box which are based on the endowments. [Hint: If Abe and Betty must each consume ribs and beer in the same proportions as each other, and if together they must consume twice as much beer as ribs, where must the contract curve lie?]
e)What is the value of the common MRS for Abe and Betty at any point on the contract curve you found?
f)If the competitive equilibrium is Pareto Efficient, then what must be the equilibrium price ratio, that is (P*Ribs/P*Beer)?
g)How much ribs and beer do Abe and Betty each consume in this competitive equilibrium? [Hint: Set the P*Beer= 1 and from that infer P*Ribs. Now, what is Abe’s income based on his endowment of ribs and beer? Given his utility function, what is his demand function for ribs and for beer? Now just plug in. Do the same for Betty. Check that is all sums up.]
h)Illustrate the competitive equilibrium in your E/B box.