Question 3
What can we deduce from \(u(x_{1},x_{2})-\lambda^{*}\left(x_{1}p_{1}+x_{2}p_{2}\right)\leq u(x_{1}(\lambda^{*}))+u(x_{2}(\lambda^{*}))+\lambda^{*}\left(p_{1}x_{1}\left(\lambda^{*}\right)+p_{2}x_{2}\left(\lambda^{*}\right)\right)\)?
True: If \(u(x_{1},x_{2})>u(x_{1}(\lambda^{*}),x_{2}(\lambda^{*}))\) then \(x_{1}p_{1}+x_{2}p_{2}>y\)
False: If \(u(x_{1},x_{2})>u(x_{1}(\lambda^{*}),x_{2}(\lambda^{*}))\) then \(x_{1}p_{1}+x_{2}p_{2}<y\)
True: If \(u(x_{1},x_{2})>u(x_{1}(\lambda^{*}),x_{2}(\lambda^{*}))\) then \(x_{1}p_{1}+x_{2}p_{2}>p_{1}x_{1}\left(\lambda^{*}\right)+p_{2}x_{2}\left(\lambda^{*}\right)\)
False: If \(u(x_{1},x_{2})>u(x_{1}(\lambda^{*}),x_{2}(\lambda^{*}))\) then \(x_{1}p_{1}+x_{2}p_{2}<p_{1}x_{1}\left(\lambda^{*}\right)+p_{2}x_{2}\left(\lambda^{*}\right)\)