Consider an economy with two possible states of the world, with associated probabilities of occurrence \((1 / 2,1 / 2)\), and a representative agent with logarithmic utility function. In the economy there are two traded assets: the first asset, with price \(p_{1}=1\), delivers a risk free payoff of 1 in correspondence of both states of the world, while the second asset, with price \(p_{2}\), delivers the random payoff \((1 / 2,2)\). Determine the equilibrium price \(p_{2}\) of the second asset when the economy's aggregate endowment is given by \(\left(e_{1}, e_{2}\right)\).\section