A Giffen good is a good whose demand increases when its price increases (at some price) While it is clearly impossible for this to happen at all prices, it is theoretically possible if the good is suf- ficiently inferior. (Potatoes in the midst of the Irish potato famine is the most oft-cited example, but even this is debated.)
(a) Illustrate diagrammatically a Giffen good, showing how the income effect dominates the substitution effect. Consider now Sheila who consumes leisure (h) and a consumption good (c), maximizing U(c, h) subject to the budget constraint c=w(T-h)+1, where T is the total time Sheila has available to either work or enjoy leisure (and I have normal- ized the price of consumption to 1).
(b) Observe that the budget constraint can be written as C+ wh=wT+1. Illustrate graphically the impace on the buget constraint of an increase in the price of leisure
(c) Under what conditions will leisure be a Giffen good (i. e., an increase in its price w leads to increase in in the consumption of leisure h)? For this part, it is enough to argue using diagrams.
(d) Suppose Sheila’s utility function is Cobb Douglas, Utc, h]= ch. What Sheila’s utility maximizing choice of leisure? Is it ever increasing in w?