Thomas has utility function U(x, y) = x^1/2y^1/2 and faces prices px = 1 and py = 1 and has income | = 10. Suppose the price of x increases to px = 4. How much does his income need to increase for him to be just as well off as before the price increase?

Recent research confirms that the demand for cigarettes is not only inelastic, but it also indicates that smokers with incomes in the lower half of all incomes respond to a given price increase by reducing their purchases by amounts that are more than four times as large as the purchase reductions made by smokers in the upper half of all incomes. How can the income and substitution effects of a price change help explain this finding?