Principles of Economics/Budget Constraints
This is the basic budget curve (often a line). Its slope is an indication of relative prices (opportunity cost of one good for another) because at any point along the line one has to give up something for more of another. The point indicated by the gray lines is one way of dividing up the budget (in quantity of money terms) between two goods (in quantity terms).
Budgets at differing incomes
Different incomes will have differing budget constraint positions. Lower incomes will be closer to the origin, while higher incomes are farther. As the graph shows, higher incomes allow one to buy more of one or both goods without necessarily having to give up some of any good.
Budgets and changing prices
When the price of the good with price along x axis (good Q1 in this case) increases in comparison with the other good, the budget constraint rotates clockwise. This is because the budget can no longer buy as much of the first good (1). When the other good's (2) price increases, the constraint rotates counterclockwise, indicating fewer bought (Q2).
Increase in cost of good 1
When there is an increase in the cost of good 1, the consequences will be most severe for one who buys all good 1 and no good 2, while it will have no effect on those who buy all good 2, hence the y intersection does not change while the x intersection changes notably. The increase moves the new x intercept closer to the origin, indicating fewer can be bought. A decrease in price would move the new x intercept to the right. If the quantity of good 1 purchased is to remain constant, some of good 2 will be sacrificed, and vice versa.
Increase in cost of good 2
When there is an increase in the cost of good 2, a similar situation occurs, except that the axes to which the changes act on are changed.