ECON2121-WE01

INTERMEDIATE METHODS FOR ECONOMICS AND FINANCE

2022

SECTION A

1.     Solve the following differential equations

In each case also i) discuss the local existence and uniqueness; ii) discuss the maximum interval of existence of the solution(s); iii) draw the integral curves to show your findings.

2.     Consider the following version of the Solow model:

where A < B. Answer the following questions:

a.   Using a phase diagram show how the number of equilibrium points depends on the threshold k(̅), ad find their value.      (40 marks)

b.   Show both analytically and geometrically the stability properties of the equilibria. (30 marks)

c.   Provide an economic interpretation of the results and explain whether and under which parameters condition a poverty trap can emerge in this model.                 (30 marks)

SECTION B

3.     Discuss the consistency of the following linear system as k  ∈ R varies and compute its solutions when the system is consistent. Base your answer on the relevant theory.

4.     Solve the following constrained optimization problem:

knowing that, in the second order conditions, for the determinant of the bordered Hessian matrix, C32 = —8z2 and C24 = 8z2 — 8λ1x2. Base your answer on the relevant theory.