There are two invididuals. The first (individual A) has the utility function \(u^{a} = x_{1}^{2} + x_{2}^{2}\) , x>=0, and endowment (1,2).
The second (individual B) has utility function \(u_{b} = x_{1} + ax_{2}\) , a>0, x>=0, and endowment (2,1).
1. Compute the competitive equilibrium prices and allocations.
2. Compute the Pareto optimal allocations.
3. Compute the core allocations.
The parameter "a" is making it difficult for me to do the computations. I think that because individual A has a convex utility function, there will be a corner solution.