consider an economy with three states the

Question

Consider an economy with three states. The following set of stocks is traded:

  x₁=(2,2,0)    x₂=(1,0,3)  x₃=(0,2,4).

The t=0 prices of these stocks are given as follows

(p₁, p₂, p₃) = (1, 1, 1).

(a)  Is there an arbitrage? 

(b)  Suppose an investment firm sells options. What is the price of a call option on stock 1 with exercise price E=1? What is the price of a put option on stock 2 with exercise price E=2.