1) There are two islands each island has a production possibility frontier given by C₁=20-.2C₀²

1. What is the endowment of each island?
2. If island 1 has a person with utility given by U(c₀,c₁)=c₀^.4c₁^.6 what is their optimal in isolation?
3. If the island 2 has person with a utility given by U(c₀,c₁)=c₀^.6c₁^.4 what is their optimal in isolation?
4. If an inter-island market opens up what are the upper and lower bounds on the interest rates to have any exchange at all?
5. What is the equilibrium rate?

2) If the Fed raises rates why would that lower inflation using just seed corn model reasoning?

3) Does it make sense that some firms borrow money to pay dividends?

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You will still turn in under the previous assignment. However,

1) It has been noted that the notation of c0,c1 switches to c1,c2 in the problem so I have fixed the typo.

2) It has been suggested to me that perhaps 1d) and 1e) are a bit hard. therefore,

a) Consider the no market solution to each person. If the interest rate plus 1 is not equal to the intertemporal rate of substitution (ratio of marginal utilities between today and tomorrow) then they will borrow or lend when adding a market. You should be able to draw this and convince yourself. Therefore, the rate must be between them or no exchange will occur.

b) When you add a market the production function changes; f(c0) becomes f(c0-B), because now the point of production (looking left to right) is c0-B not c0. To actually find the market clearing rate you must set up a system of 9 equations and 9 unknowns. There are four first order conditions for each individual and the interest rate is left as a variable too. You add the market clearing condition that borrowing sums to 0 across people (market clearing). The whole thing can be solved in excel. (I square each condition and tell excel to minimize the sum of squares by tweaking the nine parameters).

3) The last two questions are intutition, about the equation dynamics.

I hope this helps...do your best. We will go over them on Monday...Yes, I know...but, it grad school...at a Tech University...in a class called Mathematical Economics.