Budget Constraint

When goods are “free,” an individual should consume until the MU of a good is 0. This will insure that total utility is maximized. When goods are priced above zero and there is a finite budget, the utility derived from each expenditure must be maximized.

An individual will purchase a good when the utility derived from a unit of the good X (MU_X) is greater than the utility derived from the money used to purchase the good (MU_$). Let the price of a good (P_X) represent the MU of money and the MU_X represent the marginal benefit (MB_X) of a purchase. When the P_X > MB_X, the individual should buy the good. If the P_X < MB_X, they should not buy the good. Where P_X = MB_X, they are in equilibrium, they should not change their purchases.

Given a finite budget (B) or income (I) and a set of prices of the goods (P_X, P_Y, P_N) that are to be purchased, a finite quantity of goods (Q_X, Q_Y, Q_N) can be purchased. The budget constraint can be expressed,

B=P_xQ_x + P_yQ_y +…+ P_nQ_n

Where B – budget, P_n – price of N_th good, Q_n–quantity of N_th good

For one good the maximum amount that can be purchased is determined by the budget and the price of the good

Q_x that can be perchased = Budget/Price=B/P_x

The combinations of two goods that can be purchased can be shown graphically. The maximum of good X that can be purchased is B/ P_x, the amount of the Y good is B/ P_y. All possible combinations of good X and Y that can be purchased lie along (and inside) a line connecting the X and Y intercepts. This is shown in Figure.

The slope of the budget line equals the ratio of the price of good X on the horizontal axis divided by the price of good Y on the vertical axis.

Дата добавления: 2014-01-11