I have this problem and I don't know how to deal with it... No idea at all... Here it is:
Given an exchange economy of two goods and one consumer, with initial good \omega=(4,3). Show that the multi-valued function
\varphi{(p)}=B_{\omega}(p)=\left \{x \in \mathbb{R}_{+}^{2} | p \cdot x \leq p \cdot \omega  \right \}, p>>0
is continuous.