Economics and Statistics Properties of the Budget Constraint Line The budget constraint line must be a straight line because the slope of the line is the constant ratio of the prices of the two goods. Example: On the graph above, the slope of the budget line is −2, which is simply the price of pizza divided by the price of soda. The logic is that if the consumer decided to increase the consumption of pizza by one and since pizza costs $8, she will need to purchase 2 fewer sodas, since each soda costs $4. A change in income, or a proportional change in the relative prices of both goods, will result in a parallel shift (to the left or to the right) of the budget constraint line. A disproportional change in the relative prices of both goods will cause the slope of the budget constraint to change. For example, if before one slice of pizza was exchanged for two sodas, a disproportional change would mean that perhaps three sodas are now required for the same one slice of pizza. The pizza amount has stayed the same, while the soda amount has changed. Graphical Determination of Utility Maximization A graph combining an individual‘s budget constraint (what she can actually buy or her real income) and indifference curves (what she prefers to buy or which bundles yield higher utility) allows the point of maximum utility to be determined. The point of maximum utility can be seen on the following graph, where the outermost indifference curve that is tangent to the existing budget constraint line (Indifference Curve I2) touches the budget constraint line. Given the income that the individual has and her preferences, this is the point that will provide the maximum amount of utility. The individual can‘t reach any point on Indifference Curve I2 except the point where it touches the budget constraint line, because that would exceed her available income. The other points on the budget constraint line do not provide the maximum utility because they are not tangent to the highest possible indifference curve line. Therefore, by being at the point where the highest possible indifference curve is tangent to the budget constraint line, the individual receives more utility than she could receive at any other point on her budget constraint line for a given level of income
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