Consider a one-period economy with two possible states of nature at time \(t=1\). The risk-free rate in this economy is \(1 \%\). There is a project (call it project 1) in this economy with value today of 6.7 and payoffs \(\Gamma_{11}=10\) and \(\Gamma_{12}=5\)

(a) Compute the vector of state-prices when there are no arbitrage opportunities.

(b) Consider another project (project 2) with payoffs \(\Gamma_{21}=-2\) and \(\Gamma_{22}=4\). The investment necessary to do project 1 is 5 ; to do project 2 , we must invest 2 . Will an agent invest in both projects?