Economics is the study of choice, and one of the choices we all have to make is how many hours to sleep each day. One model, advanced by Professor Mohamed El Hodiri in "The Economics of Sleeping," (Manifold 17: 1975), analyzes an individual's choice between sleep and consumption. Suppose that an individual has 24 hours to allocate between work and sleep. In working, the individual receives a wage, with which she can purchase consumption goods. Suppose the individual maximizes a utility function of the form u=x2s, where x represents daily consumption and s represents hours of sleep. Also, let x=w(24−s), with w representing the wage received for each hour worked.
What is the optimal number of hours to sleep per day according to the model?