Suppose that, holding prices constant, Alice has preferences over the number of books she purchases, illustrated in the chart at right.
a. Draw a smooth approximation of Alice€™s Engel curve for books, indicating the ranges over which books are inferior goods and over which they are normal goods.
b. A luxury good is a good that has an income elasticity greater than 1. Give the ranges in which books are luxury goods for Alice.

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Income (thousands of dollars) Optimal number of books purchased 10 15 20 25 30 35 40 45 50 20 25 26 10