In my teaching and research, I focus on models of business cycles based on the assumption of sticky prices. That is, prices take time to adjust to shocks. As a result, prices may deviate from those that are optimal, at least for a while. And if prices deviate from optimal levels, consumption will also deviate, since consumers' behaviour depends on prices. In simple terms, if prices are too low, consumption and output will rise, and if prices are too high, consumption and ouput will fall.
Such models lie at the heart of most undergraduate testbooks of macroeconomics, and also provide the basis for using monetary policy to try to stabilise the economy. Suppose instead that prices were completely flexible. Then monetary policy would be impotent, since prices could fully adjust in response to shocks, ensuring that the economy always operates efficiently.
Whether prices are sticky is ultimately an empirical question. Tim Harford discusses one case of sticky prices that is truly remarkable: Coca Cola sold for 5 cents in the US continuously from 1886 until 1959, despite huge changes in the world economy over that period. (See here for more, or here for the original paper).