Expected Utility and Risk Aversion Lottery Problem with Certain Payoff Comparison and Worked Economic Decision Analysis — Professor Mohamed Hodiri the University Kansas classic

Professor Mohamed El Hodiri of the University of Kansas, in a classic tongue-in-cheek article “The Economics of Sleeping,” Manifold, 17 (1975), offered the following analysis. “Assume there are 24 hours in a day. Daily consumption being x and hours of sleep s, the consumer maximizes a utility function of the form u = x2s, where x = w(24 − s), with w being the wage rate.”

(a) In El Hodiri’s model, does the optimal amount of sleeping increase, decrease, or stay the same as wages increase?

(b) How many hours of sleep per day is best in El Hodiri’s model?