Consider an economy with three possible states of the world with equal probabilities of occurrence. The economy's aggregate endowment is given by \(e=(2,5,3)\) and there are three traded assets. The first asset is risk free, has price \(p_{1}=1\) at time \(t=0\) and delivers the constant payoff 1 at time \(t=1\). The two remaining assets are risky: the first asset has random return \(\tilde{r}_{2}=(0,3,1)\) and unitary price at time \(t=0\) and the second asset has random payoff \(\tilde{d}_{3}=(0,0,2)\) and price \(p_{3}\) at time \(t=0\). The aggregate supply of the three assets is given by \((2,1,0)\). Determine the equilibrium price of the third asset assuming that the CAPM relation holds.