Question

In this problem you will apply the utility maximization framework to try to understand some of the effects of the current banking crisis on consumers wellbeing. Take a two period model in which consumers utility function is U(C1,C2)=C1C2 where C1 is consumption in period 1 and C2 consumption in period 2, both retrieved in cash. The consumer is free to borrow or save in period one as the interest rate r, through the banking system.

a) Write the consumer's inter-temporal budget constraint, expressing C2 as the function of M1, M2, r and C1. how does the budget constraint change when r increases?

b) Solve for the consumers optimal level of C1 and C2, each as a function of incomes and the interest-rate only.

c) what is the resulting indirect utility function? show that, all other things equal, an increase in r is welcome by the consumer as long as (1+r)>M2/M1.

d) The period between 2015 and 2019 was one in which banks were offering interstates. how does the optimal choice of C1 change when r increases? all other things being equal, does an increase in the interest-rate make the consumer likelier to save more or borrow more in period 1?

e) suppose that M1=M2=1000 and suppose the interest-rate is 5%. what is the optimal choice of C1? does that make this consumer a saver?

f) what if the interstate was eased to 10%? what is the resulting optimal choice of C1? and what is the resulting maximized level of utility?

g) what happened in the banking system is that the rules change in mid course, a consumer made his decision for the C1 and C2 in period 1, consumed C1 but before period 2 came around the banking sector was in crisis, and denied all depositors access to the savings. For those consumers who were savers in period 1, this meant that after consuming C*1 in period 1, they were forced to forfeit their savings and whatever interest they could have accrued, consume only C2=M2 in period 2. what is the resulting utility after the crisis when M1=M2=1000 and r=10%? how large is the loss of utility compared to the maximized utility calculated in (f), where there was no crisis and where C2=C*2 instead of C2=M2?

h) Among suggested "settlement policies", one solution is that instead of denying depositors all of the savings, now that we are in. period 2, banks would pay 5% interest instead of 10% promised before the crisis. so in effect, for savers, C2 is now M2 and whatever the consumer saved in period 1 but was 5% interest instead of 10% applied to their savings. Calculate the utility of the consumer under this scheme. How does that compare to the utility calculated in (g)? and how does it compare utility calculated in (f)?

i) A group defending depositors rights argues that there is an additional more hidden loss of utility entailed by the scheme described in (h): the consumption level for period 1 chosen by consumers was based on an interstate of 10%, so when r is forced to be 5% in period 2 that choice of C1 is no longer optimal. Now that we are in period two and r=5%, looking back at past choices, what is the amount of "excessive" saving that C1 entailed because it was done under a regime of r=10%? What would have been the level of utility if they had known from the outset that the interest-rate was only 5%? How does that compare the utility found in (h)?

Answer 1