Suppose that a budget equation is given by p1 x1+p2 x2=m....

Suppose that a budget equation is given by $p_{1} x_{1}+p_{2} x_{2}=m$. The government decides to impose a lump-sum tax of $u$, a quantity tax on good 1 of $t$, and a quantity subsidy on good 2 of $s$. What is the formula for the new budget line?

Key Concepts

Effective Prices

Effective prices are the adjusted prices that consumers face after accounting for taxes and subsidies. They combine the nominal prices with any additional costs or benefits from government policies, guiding the consumer’s decision-making process under modified budget constraints.

Quantity Subsidy

A quantity subsidy is a per-unit payment made by the government that reduces the cost of purchasing each unit of a good. This effectively lowers the price faced by the consumer, causing a rotation of the budget line in favor of that good.

Quantity Tax

A quantity tax is imposed on each unit of a good purchased by the consumer, effectively increasing the cost per unit of that good. This alters the slope of the budget line for that good, as the effective price becomes the original price plus the tax per unit.

Budget Constraint

A budget constraint represents the combinations of goods a consumer can purchase given their income and the prices of goods. It is the fundamental equation in consumer theory that shows the trade-offs between different goods, guiding optimal consumption choices.

Lump-Sum Tax

A lump-sum tax is a fixed amount charged to a consumer that does not vary with the level of consumption. It effectively reduces the consumer's overall income regardless of their spending decisions, shifting the entire budget line downward by that fixed amount.

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