Home Assignment 1 FE

1.

Financial Economics
Homework 1
DEADLINE: 6th October 2024, 23:59
Submit to SmartLMS / [email protected] (if SmartLMS is not available).
Clearly indicate your name, group and year of study
Task 1
Consider a two-period economic model. There are two agents R and A in the
R
economy. The endowments of R are (eR
1 , e2 ) = (1, 0), the endowments of A
A
A
are (e1 , e2 )= (1, 2). The two agents trade on a bond that pays 1 in the second
period. Both agents have the utility function u(c1 , c2 ) = −e−c1 − βe−c2 . Given
β = 0.8.
a) Write down the competitive equilibrium model using the notations in the
lecture. What are the utility maximization problems? What are the marketclearing conditions?
b) Write down the Euler equations. Compute the consumptions of R and
A, interest rate, and bond price.
Task 2
Consider a two-period economic model. The agent has the following utility
function:
1
1
+β
u(c1 , c2 ) =
2
(c1 − 1) + 4
(c2 − 4)2 + 1
The endowment is (e1 , e2 ) = (5, 0). Given β = 0.5. Storing of good does not
affect its the quality.
a) Write down agents’s simple saving model using the notations in the lecture. What is the ‘real interest rate’ in this example? Find c1 , c2 and r.
b) Redo the calculations with the endowment (e1 , e2 ) = (8, 0). What is the
result? How can you explain it?