Consider an economy with two dates (t=0,1) and three states at t=1. The following three assets are traded:

Asset A Asset B Asset C

xA=(2,0,0) xB=(0,3,4) xC=(1,0,2)

pA = $1.20 pB = $3.10 pC = $X

In questions (a) to (c) suppose X=$1.40

1. (a) Is there an arbitrage? [4p]

2. (b) Design a portfolio with payoff (8,6,12) and what is the price of that portfolio? [8p]

3. (c) Suppose a start-up company wants to go public. The firm has total costs of $100,000 at date t=1 and sales of $120,000 in state 1, $140,000 in state 2, and $230,000 in state 3. The firm wants to issue 1,000 IPO shares. (A share is endowed with a cash flow right of 0.1% of the total profits of the firm.) Should the underwriter optimally suggest an IPO price of $82 per share? [6p]

4. (d) Find the full set {X} for pC such that there is no arbitrage. [6p]