Question 4
Drag the following two verbal statements into the category given by the
mathematical statements:
Category 1 If
\(u(x_{1},x_{2})>u(x_{1}(\lambda^{*}),x_{2}(\lambda^{*}))\) then
\(x_{1}p_{1}+x_{2}p_{2}>y\)
If the pair \((x_{1},x_{2})\) gives strictly higher utility than the
pair
\(\left(x_{1}\left(\lambda^{*}\right),x_{2}\left(\lambda^{*}\right)\right)\),
then \((x_{1},x_{2})\) is not affordable.
Category 2 If
\(u(x_{1},x_{2})>u(x_{1}(\lambda^{*}),x_{2}(\lambda^{*}))\) then
\(x_{1}p_{1}+x_{2}p_{2}<y\)
Category 3 If
\(u(x_{1},x_{2})>u(x_{1}(\lambda^{*}),x_{2}(\lambda^{*}))\) then
\(x_{1}p_{1}+x_{2}p_{2}>p_{1}x_{1}\left(\lambda^{*}\right)+p_{2}x_{2}\left(\lambda^{*}\right)\)
If the pair \((x_{1},x_{2})\) gives strictly higher utility than the
pair
\(\left(x_{1}\left(\lambda^{*}\right),x_{2}\left(\lambda^{*}\right)\right)\),
then \((x_{1},x_{2})\) is more expensive than
\(\left(x_{1}\left(\lambda^{*}\right),x_{2}\left(\lambda^{*}\right)\right)\).
Category 4 If
\(u(x_{1},x_{2})>u(x_{1}(\lambda^{*}),x_{2}(\lambda^{*}))\) then
\(x_{1}p_{1}+x_{2}p_{2}<p_{1}x_{1}\left(\lambda^{*}\right)+p_{2}x_{2}\left(\lambda^{*}\right)\)