Here is the following extension of the three date Diamond-Dybvig model: agents can invest in following three possible technologies

-a short-term investment at date 0, that yields a return r1 =1 at date 1.

-a long term investment at date 0, that yields a return R > 1 as of date 2 but can also be liquidated at date 1 for a return L

-a short-term investment at date 1, that yields a return r2 at date 2. However, r2 is observed only at date 1.
It is assumed that :1

Note the consumption profile (C1;C2) will depend on r2; as depending on r2 agents may choose to invest in the short-term investment in date 1.

a.Describe and discuss how consumption planning C1 and C2 may change in comparison with the standard Diamond-Dybvig model without the short-investment available at date 1.

b.The short-term investment opportunity with r2; means that the agents are exposed to interest rate risk. Discuss, why, if r2 is low, the agents will not invest in date 1 in the short-term investment, and will not be exposed to any interest rate risk.

c. Now assume that all the agents deposit their endowments to form a bank. The bank has the same three investment technologies described above. Discuss if the exposure to interest rate risk of r2 increases or decreases the stability of the bank.