General Equilibrium.

[NM]

Can someone please confirm the answers to the following question?

Q.>> Bob has an initial endowment consisting of 10 units of food and 10 units of clothing.  Eric has an initial endowment of 10 units of food and 20 units of clothing. Draw an Edgeworth Exchange Box for these consumers.

Bob regards food and clothing as perfect one-for-one substitutes, while Eric regards them as perfect complements but in a ratio of 3 units of clothing for 2 units of food.  What is the set of allocations that are pareto-preferred or pareto superior to the original endowment given above?  Where is the contract curve in the EEB?  What set of trades could lead to the contract curve? What price ratio would be required to ensure that a competitive equilibrium reaches the contract curve from the initial endowment?


Thanks :)

[Dreyfus]

The entire diagnol of Edgeworth box is Contract curve.
The price ratio must be Pf/Pc = 3/2
Eric will buy Fish and sell cloths and Bob will sell Fish and buy cloths!

[hs]

i think price ratio shud be 1

[Dreyfus]

For the price ratio i m not sure as i did it by taking an arbitrary allocation on contract curve where both individuals are better off from their initial endowments.

[NM]

As per my calculations, the price-ratio is coming out to be 2/3.

[SoniaKapoor]

How did u solve Nm?

[NM]

From the given data we can form the utility functions as:

Ub=Fb+Cb and Ue=min(2Fe, 3Ce)

Now when we derive the demand curves by taking P1=1, we get:

Bob: 10(1+P2)/P2 and Eric: 2(10+20P2)/(3+2P2)

Equating the demand equal to supply, I am getting P2= 3/2, which gives P1/P2 = 1/(3/2) = 2/3.

Someone please check, I am not sure of this though.

[mrittik]

i thnk price ratio shld be 1...bcoz price ratio always dominated by substitution....lets check

[Granpa Simpson]

Answer 1: The entire diagonal will be the contract curve.
Answer 2: Pareto Superior allocation makes atleast one person better off as compared to the initial endowment point. Here Bob has initial endowment (10,10) and his utility function can be considered as U=x+y with an initial utility level of 20, similarly eric has an initial endowment of (10,20) with the utility function U=Min{x/a,y/b} where a/b=3/2=1.5 with an initial utility level of 10, clearly Eric has 5 extra amount of y then is needed, so what he can do is that he can trade this y for x till he reaches an utility level higher than the original one. In this case if he trades 2 units of y for 2 units of x, his new utility will be U=Min{12,18}, clearly now x and y are in the ratio 3/2 and Eric's utility is increased to 12. So such an allocation will be considered as a Pareto Superior move where atleast one agent is made better off without making the other worse off, see here that due to the aforesaid reallocation Bob gets (8,12) and is on the same utility level of 20 while eric moves on to the utility level of 12. Thus this is a Pareto Superior move.
Answer 3: From the previous part it can be easily said that the price ratio should be (px/py)=1.
Akshay plz check.

[NM]

Alright.

I made a mistake with Eric's utility function. But in your solution shouldn't a/b be equal to 2/3?!

((As it is given that Food/Clothing=2/3))

[Granpa Simpson]

Consider x=Food and y=Clothing,
Now his initial endowment in (10,15).
For Eric, it is given that for 2 units of food 3 units of clothing is needed.
Using unitary method we get for 1 unit of food (3/2)=1.5 units clothing is needed.
So for 10 units food 10*1.5=15 units of clothing is required to attain the definition of complementarity.
Hope this helps.