INTERMEDIATE MICROECONOMICS 2. Consumer Theory (cont'd) 2.3 Constraints No matter taste or preference, to acquire utility a consumer must obtain goods.  With the exception of 'free goods', a consumer must pay a price.  To pay a price a consumer must have an income.  To obtain income a consumer must work, i.e. suffer disutility.  In other words, a consumer can only obtain utility, no matter taste or preference, subject to income and price constraints.  Given a specific level of income (I) and assuming there are only two goods (x & y) and further assuming prices are Px and Py respectively, then a budget line can be plotted showing all commodity combinations of x and and y  that can be purchased by a consumer (M&Y 10th  Fig. 3.6; M&Y 11th Fig. 2.7; B&Z Fig. 3.8; B&B Fig. 4.1).  The slope of the budget line is the negative of  the 'price ratio' or - (Px/Py).  By convention, the price ratio is defined as Px/Py.  The intercepts represent the maximum amount of either good that a consumer could purchase if all of I was spent on one or the other commodity. The consumer can consume anywhere along the budget line and anywhere below it.  Only an irrational consumer would, however, consume below the budget line.  The consumer cannot, however, consume above the budget line because of the income constraint. If income goes up (and x and y are normal goods) a new and higher budget line becomes available to the consumer parallel to the original, assuming Px and Py remain constant (M&Y Fig. 3.7; B&Z Fig. 3.9; B&B 4.2).  The slope of the budget line remains the same but the intercepts are higher on each axis.  If Px (or Py) declines then the price ratio changes and the slope of the budget line changes (M&Y 10th Fig. 3.8; M&Y 11th Fig. 2.9; B&Z Fig. 3.10; B&B Fig. 4.3)). Assuming I and Py remain constant then the original y-intercept remains fixed at the original point because the maximum amount of y that can be purchased remains the same.   The x-intercept, however, increases, that is, the consumer can buy a larger maximum of x with the same I. The budget line's intercept on the y-axis will not vary from this specification in the case of normal or inferior nor complementary or substitute goods.  A given income can purchase a maximum of either x or y no matter the nature of these commodities.

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