When I took a course in consumer theory, the economy always had a single consumer, represented by a monotone positive utility function $u(x,y)$ and an income $I$. Given prices $p_x$ and $p_y$, it is possible to calculate the demands of the consumer for products $x$ and $y$.
Now, I deal with a different type of economy: there are many consumers, each of them wants only a single unit of each product. Each consumer is represented by three positive values: $u_x$ (utility for having $x$), $u_y$ (utility for having $y$) and $u_{xy} \geq \max(u_x,u_y)$ (utility for having both $x$ and $y$). Given prices $p_x$ and $p_y$, each consumer buys either $x$ or $y$ or both, whichever gives the highest net utility (utility of product/s minus price). So it is possible to calculate the aggregate demands for $x$ and $y$.
MY QUESTION IS: Is there a natural/standard way to convert between these two types of economies?
I.e, given a utility function $u(x,y)$ and income $I$ for a single consumer, is it possible to construct a set of consumers with different $u_x$, $u_y$ and $u_{xy}$, such that the demand curves in both economies are the same?