Originally the consumer faces the budget line p1 x1+p2 x2=m...

Originally the consumer faces the budget line $p_{1} x_{1}+p_{2} x_{2}=m .$ Then the price of good 1 doubles, the price of good 2 becomes 8 times larger and income becomes 4 times larger. Write down an equation for the new budget line in terms of the original prices and income.

Key Concepts

Budget Line Transformation

When both prices and income change proportionally, the budget line undergoes a transformation that reflects these combined effects. Analyzing such transformations is important in understanding how changes in economic conditions impact consumer choices and the affordability of various consumption bundles.

Effects of Income Changes

Changes in income shift the budget line without affecting its slope, provided that prices remain constant. An increase in income shifts the line outward, thereby expanding the set of affordable consumption bundles, and vice versa for a decrease in income.

Budget Constraint

The budget constraint represents the combinations of goods a consumer can purchase given their limited income and the prices of the goods. It is typically expressed in an equation that sets total expenditure equal to income, indicating the trade-offs between the goods available to the consumer.

Effects of Price Changes

Price changes alter the slope of the budget line by changing the relative prices of the goods. When the price of a good increases, it becomes relatively more expensive, which can shift the consumer's optimal choice and change the opportunity cost between goods.

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