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Explain the full effect of a change in income on the quantity of good X consumed. In other words, explore (as best as you can) how a change in income will affect the willingness to buy good X.

Erample 3.1: Quasi-Linear Preferences "imppose there are two goods r and y, whose quantities must be non negative, and whose prices are p and q respectively, both be- ing, positive. Consider a consumer with income I and the utility function U(x, y) = y + a In(x), where a is a given positive constant. Such preferences are called quasi-linear, because the utility function can be chosen linear in I h quantity of one of the goods. To find this consumer's demand functions, we can use the Inlin-Tucker Theorem. Form the Lagrangian L(x, y, A) = y ta In(@)+A[I-px - qy]