Please help with all the parts. Thanks!

Question 1 (24 points) Consider an economy with two dates (t=0,1) and three states at t=1. The following three assets are traded: Asset A XA (2,0,0) PA = $1.20 Asset B XB-(0,3,4) PB = $3.10 Asset C Xc=(1,0,2) Pc = $x In questions (a) to (c) suppose X=$1.40 (a) Is there an arbitrage? [4p) (6) Design a portfolio with payoff (8,6,12) and what is the price of that portfolio? [8pl (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) (d) Find the full set {X} for pc such that there is no arbitrage. [6] Question 1 (24 points) Consider an economy with two dates (t=0,1) and three states at t=1. The following three assets are traded: Asset A XA (2,0,0) PA = $1.20 Asset B XB-(0,3,4) PB = $3.10 Asset C Xc=(1,0,2) Pc = $x In questions (a) to (c) suppose X=$1.40 (a) Is there an arbitrage? [4p) (6) Design a portfolio with payoff (8,6,12) and what is the price of that portfolio? [8pl (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) (d) Find the full set {X} for pc such that there is no arbitrage. [6]