Consider an economy populated by \(I\) agents with exponential utility functions of the form

\[u^{i}(x)=-\frac{1}{a_{i}} \mathrm{e}^{-a_{i} x}, \quad \text { with } a_{i}>0 \quad \text { for all } i=1, \ldots, I .\]

Suppose that there are two traded assets: a risk free asset with rate of return \(r_{f}\) and a risky asset with return distributed according to a normal law with mean \(\mu\) and variance \(\sigma^{2}\). Suppose that the aggregate supply of the risky asset is equal to 1 . Determine the risky asset risk premium in correspondence of an equilibrium of the economy.