What is Atom economy?

Example 48.12 (Addition against substitution)

Bromoethane from ethene, $\ce{C2H4 + HBr -> C2H5Br}$: every atom ends up in the product, atom economy $108.9/(28.0 + 80.9) = 100\,\%$. Ethanol from bromoethane, $\ce{C2H5Br + NaOH -> C2H5OH + NaBr}$: the atom economy is $46.0/(108.9 + 40.0) = 30.9\,\%$; per kilogram of ethanol, $2.2\,\mathrm{kg}$ of sodium bromide. An addition always has an atom economy of $100\,\%$; a substitution or an elimination never does.

Example 48.15 (Two routes to ibuprofen)

Ibuprofen, $\ce{C13H18O2}$, is made from the hydrocarbon $\ce{C10H14}$ (isobutylbenzene). The older route uses six steps and, in each, a full amount of reagent; added together, its reactants have a molar mass sum of $514.5\,\mathrm{g}/\mathrm{mol}$, for $206.0\,\mathrm{g}/\mathrm{mol}$ of ibuprofen: atom economy $40\,\%$. The newer route uses three steps, two of them catalysed, and the overall equation

gives $206.0/266.0 = 77\,\%$. Its by-product, ethanoic acid, is recovered and used: counted as a product, the atom economy exceeds $99\,\%$.