What is the basic Economic problem, and how does Economics as a discipline approach this?

The basic economic problem is usually defined as there being a situation of scarce resources but an unlimited or infinite number of wants and demands for these resources. Economics as a discipline seeks to ask how these resources are allocated, and the role that governments and other economic players can play in determining how these resources are allocated.
For example, there are a finite number of houses in the UK, but there exists an infinite demand for these houses. Economics will examine the role of price in making sure that demand for housing is equal to supply of housing. Economists will also look at the efficiency with which the houses are allocated amongst buyers - are they being allocated in a way which maximises welfare? Is there a wastage of resources occurring? - and determine ways in which economic actors can further improve the efficiency of this market.