Bobby is a college student who has $500 of income to spend each semester on books and pizzas. The ...

Without the gift certificate, Bobby's budget constraint is indicated by the line segment from 10 books and 0 pizza to 0 books and 50 pizzas (labeled BC1).  With the gift certificate that can only be used for book purchases, Bobby still cannot afford anymore than 50 pizzas.  However, he is guaranteed 6 books even if he spends all his money on pizza.  Since the price of books and pizza hasn't changed, the slope of his new budget constraint is the same as the slope of the old budget constraint.  The new budget constraint is drawn above as BC2.  Note that with the gift certificate, Bobby has an expanded opportunity set and is guaranteed more of both goods no matter what his original consumption choice on BC1 was.  This implies that Bobby is strictly better-off with the gift certificate.