A working model of Supply and Demand
Industrial Organization is the field concerned with estimating supply and demand relationships in individual product markets. You can see for example Einav and Levin for a description of what empirical IO people are up to. The specific models are usually much more complicated than what you learn in Mankiw, tailored to specific markets, and very strong assumptions are required to estimate them. For recent IO papers, you can see for example the NBER working paper series.