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A commonly used example is intercity bus service. Those with more money will fly, or take the train.
Depending on the indifference curves, the amount of a good bought can either increase, decrease, or stay the same when income increases. In the diagram below, good Y is a normal good since the amount purchased increases from Y1 to Y2 as the budget constraint shifts from BC1 to the higher income BC2. Good X is an inferior good since the amount bought decreases from X1 to X2 as income increases.

See also normal goods, giffen goods, consumer theory