5SSPP217: Microeconomics
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5SSPP217: Microeconomics
Coursework
Due on November 23rd, 3pm UK time
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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 Ci(t) the consumption
student i = A; B enjoys in period t = 1; 2: Similarly, denote by Mi(t) the stipend
the two students receive from their parents each period. In addition to that, Alice and Bob can borrow money from Damienís bank at interest rate rb. Alice and Bob can also deposit their savings in Damienís bank. Because Damien is their friend, heo§ers 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 ináation rate will be π:
1. [14 points] Find the expression for Aliceís intertemporal budget con-
straint as a function of MA(t) , rb ; rs and π and represent it graphically.
2. [14 points] Aliceís preferences over present and future consumption are
represented by the utility function uA (CA(1); CA(2)) = (CA(1)
A(2)
. Use the
Lagrange method to Önd her optimal consumption in each period as a
function of MA(t) , rb ; rs and π . Calculate Aliceís optimal consumption for
the case MA(1) = MA(2) = 100; rb = 0:1; rs = 0:12 and π = 0:1:
3. [12 points] Suppose that a new report from the Bank of England shows that ináationary pressures will ease out and it is expected that π = 0:06: What will be Aliceís optimal consumption in each period? How does her present and future consumptions change compared to the case π = 0:1? Represent both the old and new choices graphically. Discuss the sign (direction) of the substitution and income e§ectsresulting from the change in ináation expectation.
4. [14 points] One day at the pub, Bob jokingly tells Alice that after the new ináation report he feels as if the Bank of England had given them a raise in their parentsístipend. Alice agrees, and when she returns home, she wants to quantify that supposed raise in her stipend. Suggest Alice a method to approach and solve this problem.
5. [14 points] Bob is a very future-oriented person. For him, it is always the case that 1 unit of future consumption is as good as 3 units of present consumption. Alice enjoys teasing Bob, claiming that his intertemporal preferences are not convex like hers. Bob becomes slightly annoyed and disagrees with Aliceís statement. So, the question arises: Who is correct? Give an answer as formal as possible.
6. [16 points] Write a utility function that represents Bobís preferences. Find the expression for Bobís intertemporal budget constraint. Find Bobís
optimal consumption in each period as a function of MB(t) , Tb ; Ts and π
under that utility function. Compute his optimal consumption for the
case MB(1) = 50; MB(2) = 100; Tb = 0:1; Ts = 0:12 and π = 0:1; and for the
case when ináation becomes π = 0:06; everything else equal.
7. [16 points] Damien is wondering whether he could increase his bankís proÖts. Maybe he is o§ering his friends a too high or too low interest rate for their savings? In the international capital market, Damien can obtain a return of TD = 0:2 for the deposits his two friends make on his bank. On the other hand, Damien would not like to o§er his friends an interest rate for their savings Ts lower than Tb : Damien seeks your advice about what savings rate Ts he should o§er his friends. Damien asks you to produce supporting Ögures to aid his decision.
2023-11-20