Final Mock Exam of Econ

FINA 6282

Economics for Finance Practice

Mock Examination

Chinese University of Hong Kong

Please write your name and student number (If you don't have a student number yet, please put your application number) on the booklet.

Please answer all of the following questions. The full mark for exam is 100.

Please present the definitions, theorems and steps of the proofs clearly.

Please make sure that people can read your handwriting. You will have THREE hours for the exam.

1

Consider the following game between two firms, Sony and Toshiba.

Toshiba

Invest Heavily

Slacken

Sony

Invest Heavily

0, 0

3, 1

Slacken

1, 3

2, 2

a) Find the pure-strategy Nash equilibrium or equilibria.

b) Compute the mixed-strategy Nash equilibrium. As part of your answer, draw the best-response function diagram for the mixed strategies.

c) Suppose the game is played sequentially, with Sony moving first. What are Toshiba's contingent strategies? Write down the normal and extensive forms for the sequential version of the game.

d) Using the normal form for the sequential version of the game, solve for the Nash Equilibria.

e) Identify the proper subgames in the extensive form for the sequential version of the game. Use backward induction to solve for the subgame-perfect equilibrium. Explain why other Nash equilibria of the sequential game are "unreasonable".

(Nicholas and Synder Ch5, Q5.7)

2

Consider the following Bertrand competition model with differentiated products. Let the demand curves for firms A and B be given by:

and let the firms' marginal costs be constant, given by cA and cB respectively.

a) Find the best-response function for firm A and firm B.

b) Graph the two best - response functions. Find the Nash equilibrium assuming cA = cB = 0 algebraically and indicate it on the graph.

c) Indicate on the graph where analogue to the Stackelberg equilibrium might be, with firm A choosing price first and then firm B. Is