When analyzing the securitization equilibrium with repo lending \((0The demand for long assets \(D_{n}\) from these noise traders follows a simple demand function which is the inverse of asset price and subject to a demand shock, \(\sigma\), \[
D_{n}\left(P_{2}\right)=N\left(\frac{1-\sigma}{P_{2}}\right)\]
The demand for long assets \(D_{b}\) from the banks after liquidation equals banks' total asset holdings, \[D_{b}\left(P_{2}\right)=N d-S .\]
The aggregate supply of the long assets is just the number of projects. Therefore, by market clearing condition, \[
D_{n}\left(P_{2}\right)+D_{b}\left(P_{2}\right)=N .
\]

(a) Compute the equilibrium asset price \(P_{2}\).

(b) Assume that the parameter values ensure that \(P_{2}\) is always positive, \(P_{2}>0\). How does the demand shock from noise traders, \(\sigma\), affect \(P_{2}\) ?

(c) Show that \(P_{2}\) is more sensitive to \(\sigma\), when \(h\) is small.