Question

This problem set tells the story of three friends Alice, Bob, who are two students, and Damien, who is a banker. Alice and Bob live over two periods and care about consumption in each of them. Denote by Cit​ the consumption student i=A,B enjoys in period t=1,2. Similarly, denote by Mit​ the stipend the two students receive from their parents each period. In addition to that, Alice and Bob can borrow money from Damien's bank at interest rate rb​. Alice and Bob can also deposit their savings in Damien's bank. Because Damien is their friend, he offers them a savings account with interest rate rs​>rb​. Assume that the price of present consumption is just 1. All three friends expect that the inflation rate will be π.

1. Find the expression for Alice's intertemporal budget constraint as a function of MAt​,rb​,rB​ and π and represent it graphically.

Answer 1

Alice's intertemporal budget constraint takes into account her consumption, stipends, interest rates for borrowing and saving, and anticipated inflation. It is expressed mathematically and can be illustrated graphically as a straight line on a graph where present consumption is on the x-axis and future consumption is on the y-axis.

Step-by-step explanation:

The intertemporal budget constraint for Alice can be expressed by incorporating her options for saving and borrowing.

First, we calculate Alice's consumption in the first period (CA1), which equals the stipend received in the first period (MA1) plus the amount borrowed from the bank (B), taking into account that borrowing incurs interest that will be paid in the second period at the rate of rb.

In the second period (CA2), Alice's consumption equals the stipend received (MA2), plus the interest from any savings deposited in the first period at the rate of rs, minus the amount borrowed in the first period plus interest. The interest rates are adjusted for the expected inflation rate (π) so that savers earn (1+rs)/(1+π) and borrowers pay (1+rb)/(1+π).

The constraint can be expressed as follows:

CA1 + (CA2/(1+π))/(1+rs) ≤ MA1 + (MA2/(1+π))/(1+rs)

Graphically, this constraint is represented as a downward-sloping straight line on a graph with present consumption on the x-axis and future consumption on the y-axis. The slope of this line is determined by the ratio of the adjusted interest rates.