<p>For a continuous version of a bliss point we can have the function:
 <span class="math-container">$$U(x_1,x_2)=-(x_1-\delta)^2-(x_2-\delta_2)^2$$</span></p>

<p>where <span class="math-container">$\delta_1$</span> and <span class="math-container">$\delta_2$</span> are bliss requirements.</p>

<p>The corresponding Marshallian:                                                                                                                                               demands for <span class="math-container">$x_1$</span> and <span class="math-container">$x_2$</span> are:</p>

<p><span class="math-container">$$x_1(p_1,p_2,I)=\frac{p_1m+p_2^2\delta_1+p_1\delta_2}{p_1^2+p_2^2}$$</span></p>

<p><span class="math-container">$$x_2(p_1,p_2,I)=\frac{p_2m+p_2^2\delta_2+p_2\delta_1}{p_1^2+p_2^2}$$</span></p>

<p>The corresponding Hicksian Demands for this function is:</p>

<p><span class="math-container">$$x_1^c=\delta_1-\left[\frac{\bar{U}}{1+\frac{p_2}{p_1}}\right]^\frac{1}{2}$$</span></p>

<p><span class="math-container">$$x_2^c=\delta_2-\left[\frac{\bar{U}}{1+\frac{p_1}{p_2}}\right]^\frac{1}{2}$$</span></p>

CC BY-SA 4.0
2019-11-08T01:28:36.010Z
2019-11-08T02:14:23.450Z
2019-11-08T02:14:23.450Z
EconJohn
<p>An answer that meets all the current demands of the question:</p>

<p>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
$$
D_x(I,p_x,p_y) = \left\{
\begin{array}{cc}
x_b &amp; \mbox{ if } p_x \cdot x_b + p_y \cdot y_b \leq I \\
\left[0,\frac{I}{p_x}\right] &amp; \mbox{ if } p_x \cdot x_b + p_y \cdot y_b &gt; I.
\end{array}\right.
$$</p>

CC BY-SA 3.0
2016-10-16T18:27:42.933Z
I suspected a peicewise function of sorts. Amazing.
EconJohn
CC BY-SA 3.0
2016-10-16T18:20:08.250Z
2016-10-16T18:20:08.250Z
Giskard
<p>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? </p>

CC BY-SA 3.0
2016-10-16T18:22:30.753Z
The question is somewhat unclear. There are several such utility functions. And Marshallian demands would depend strongly on the exact preferences, so I am not sure what kind of answer you expect.
Giskard
<microeconomics><consumer-theory>
Utility function used to indicate bliss point
EconJohn
# Utility function used to indicate bliss point

(Asked by: username_0 on 2016-10-16)

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?

**Tags:** microeconomics, consumer-theory
> **Comments:**
> **username_1**: The question is somewhat unclear. There are several such utility functions. And Marshallian demands would depend strongly on the exact preferences, so I am not sure what kind of answer you expect.  

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## 2 answers

### Answer by username_1 on 2016-10-16. Score: 2 | Accepted answer

An answer that meets all the current demands of the question:

Let $(x\_b,y\_b)$ be the blisspoint. Let
$$
U(x,y) = \left\{
\begin{array}{cc}
1 & \mbox{ if } (x,y) = (x\_b,y\_b) \\
0 & \mbox{ if } (x,y) \neq (x\_b,y\_b).
\end{array}\right.
$$
The demand function for $x$ in this case is
$$
D\_x(I,p\_x,p\_y) = \left\{
\begin{array}{cc}
x\_b & \mbox{ if } p\_x \cdot x\_b + p\_y \cdot y\_b \leq I \\
\left[0,\frac{I}{p\_x}\right] & \mbox{ if } p\_x \cdot x\_b + p\_y \cdot y\_b > I.
\end{array}\right.
$$

> **Comments:**
> **username_0**: I suspected a peicewise function of sorts. Amazing.  

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### Answer by username_0 on 2019-11-08. Score: 1

For a continuous version of a bliss point we can have the function:
$$U(x\_1,x\_2)=-(x\_1-\delta)^2-(x\_2-\delta\_2)^2$$

where $\delta\_1$ and $\delta\_2$ are bliss requirements.

The corresponding Marshallian: demands for $x\_1$ and $x\_2$ are:

$$x\_1(p\_1,p\_2,I)=\frac{p\_1m+p\_2^2\delta\_1+p\_1\delta\_2}{p\_1^2+p\_2^2}$$

$$x\_2(p\_1,p\_2,I)=\frac{p\_2m+p\_2^2\delta\_2+p\_2\delta\_1}{p\_1^2+p\_2^2}$$

The corresponding Hicksian Demands for this function is:

$$x\_1^c=\delta\_1-\left[\frac{\bar{U}}{1+\frac{p\_2}{p\_1}}\right]^\frac{1}{2}$$

$$x\_2^c=\delta\_2-\left[\frac{\bar{U}}{1+\frac{p\_1}{p\_2}}\right]^\frac{1}{2}$$


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