Finding restrictions on parameters for a demand function
Demand is positive, so $A&gt;0$.
If $p_1$ goes to $\infty$, $x_1$ has to go to 0, since $p_1x_1$ is bounded by $M$. Thus $\alpha &lt; 0$.
If $p_2$ goes to 0, $x_1$ cannot go to $\infty$, since $p_1x_1$ is bounded by $M$. Thus $\beta\ge 0$.
If $M$ goes to 0, $x_1$ has to go to 0, since $p_1x_1$ is bounded by $M$. Thus $\gamma &gt; 0$.
If both prices and income are scaled up by the same factor, then demand doesn't change, so $\alpha+\beta+\gamma=0$.