Problem
A consumer's income in the current period is 500 and income in the future period is 600. There would be no taxes for current and future. The real interest rates are 4% for lending. Also assume that the current and future consumptions are perfect 1-for-1 complements, or the consumer wants to consume 1 unit of current consumption and 1 unit of future consumption.
A bank's profit under imperfect information in credit markets can be expressed as follow:
Π = aL(1+r2 ) - L(1+r1),
where a = proportion of good borrowers,
L = amount of loan, r1 = loan lending interest rate, r2 = loan borrowing interest rate,etc
Assume that the market is in an equilibrium and the bank's profit would be zero. The proportion of good borrowers is 90%.
1) Compute r2 based on the given information above.
2) Compute the optimal choice for this consumer and graphically show all (endowment, current and future consumption, and savings etc).
3) Show graphically how the consumer's welfare decreases when market uncertainty increases.