Difference between budget set and budget …

Budget Set:

Budget set refers to the attainable combinations of a set of two goods, given prices of the goods and income of the consumer.   A budget set is based on the assumptions that income of the consumer and the prices of two goods (consumed by the consumer) remain unchanged. Accordingly, a change, either in prices or in consumer's income will lead to a change in the budget set.

Budget Line: 

A budget line is a line that shows the maximum amount of good-X or of good-Y (or the possible combinations of X and Y) that the consumer can buy, given his money income and the prices of the goods X and Y. It is also called Price Line, as it shows the price ratio between good-X and Good-Y, or the rate at which one good can be exchanged for the other, given prices of the two goods in the market.  The position of the budget line depends on the income of the consumer and prices of the two goods. If prices of two goods remain unchanged, then with an increase in income, budget line of the consumer shifts to the right. Similarly, if income of the consumer remains unchanged, the budget line will shift to the right when there is a proportionate fall in the prices of both goods X and Y. Thus, if the prices of both X and Y are reduced to half, the budget line will shift to the right showing twice the possible purchase of X and Y than before.