Utility function used to indicate bliss point How does one create a utility function to indicate existence of a bliss point? what do the goods marshillian demands look like in such a situation?
An answer that meets all the current demands of the question:

Let $(x_b,y_b)$ be the blisspoint. Let
$$
U(x,y) = \left\{
\begin{array}{cc}
1 &amp; \mbox{ if } (x,y) = (x_b,y_b) \\
0 &amp; \mbox{ if } (x,y) \neq (x_b,y_b).
\end{array}\right.
$$
The demand function for $x$ in this case is
$$
D_x(I,p_x,p_y) = \left\{
\begin{array}{cc}
x_b &amp; \mbox{ if } p_x \cdot x_b + p_y \cdot y_b \leq I \\
\left[0,\frac{I}{p_x}\right] &amp; \mbox{ if } p_x \cdot x_b + p_y \cdot y_b &gt; I.
\end{array}\right.
$$