The economic computer is a human computer, in the sense of "human computation" (http://goo.gl/LtEVLp): it is a system in which human agents play computationally salient functional roles. The things we do as we assist in both the production and consumption of various goods are operations in the economic computing machine. This includes our buying and selling and claiming of ownership over various things in competitive markets, yes, but it also includes the eating of a meal and the using of a pen and the chopping of a tree. Those particular behaviors are activities through which we each participate on a continuous basis with the operations of the economic computer.
You are a component of this massive machine. Right this moment, you are doing its computing work.
The economic computer can be optimized like any other computer to fit a variety of constraints and conditions. We can optimize the machine to maximize potential wealth, or to distribute resources equitably, or to minimize environmental disruption. Like any other computer, such optimization proceeds by revising the set of operations for carrying out a computation, or changing the computations being performed, or improving the hardware to facilitate certain important computations. In other words, it proceeds by making the components of the system adjust their computing behavior.
Economists have traditionally limited themselves to a very narrow set of tools with which to reprogram our economic computing environment. Issues like "the rate of interest" address a vanishingly small class of operations of the computer; indeed, the class of operations dealing with financial or proprietary exchange as a whole is but a small subset of the total set of operations the economic computer undergoes. Even the most expansive conceptual tool of economics, the "market", provides a framework only for addressing a very restricted set of operations. Imagine debugging a computer by only looking at the activity in a fraction of the registers, or providing medical care on the basis of only what was visible from inspecting the ears, nose, and throat.
If economics is to do something useful in the digital age, it should aspire to function more like debugging operations familiar from other kinds of computer engineering. It would occupy itself with determining the relevant classes of operations performed by the computer as it evolves, and how to optimize those operations for some set of constraints. It would be, in other words, a form of engineering for this particularly complex and fascinating machine.