p Time endowment is fixed at p p

最适商品税 p Time endowment is fixed at: p 预算约束:

最适商品税: p If all commodities can be taxed, imposing equal ad-valorem tax rates yields:

最适商品税: 拉姆齐法则（Ramsey Rule） p 边际超额负担 n n The additional inefficiency from incrementally raising a tax by a small amount Figure 14. 1 shows the initial excess burden as a triangle (abc) and the marginal excess burden as a trapezoid (fbae)

Figure 14. 1

最适商品税: 拉姆齐法则（Ramsey Rule） The marginal excess burden of taxing good X is approximately: ΔX. p The marginal tax revenue raised is approximately: X 1. p Therefore the marginal excess burden per dollar of tax revenue is: p

最适商品税: 拉姆齐法则（Ramsey Rule） Similar reasoning is used for good Y. p Optimization therefore leads to: p p Ramsey Rule says that to minimize total excess burden, tax rates should be set so the percentage reduction in the quantity of each good demanded is the same.

最适商品税: 拉姆齐法则（Ramsey Rule） p Recall the formula for excess burden for good X: 政府的目标函数：to minimize total excess burden by choosing taxes on goods X and Y p 约束条件： 财政收入 p

最适商品税: 拉姆齐法则（Ramsey Rule） p Setting up the La. Grangian:

最适商品税: 拉姆齐法则（Ramsey Rule） p Solving leads to a relationship between tax rates and elasticities: p Or rearranging, we have the inverse elasticity rule: 税收的效率要求： 弹性较小的商品，课征相对高的税

公平考虑 p Is it “fair” to tax inelastic goods like food and medicine? n Clearly, it is not. 纵向公平：在支付能力不同的人之间分配税赋 p vertical equity: It should distribute burdens fairly across people with different abilities to pay. p

公平考虑 Ramsey Rule has been modified to account for the distributional issues. p Degree of departure from original rule depends on: p n n How much society cares about equity Extent to which consumption patterns of rich and poor differ

横向公平 p p Horizontal equity: People in equal positions should be treated equally 境况相同的人应得到同等对待 n Measures represent outcomes of people’s decisions, so it is difficult to figure out whether they were initially in equal position.

公共部门定价 p 政策选择: n n 按平均成本定价 Average cost pricing: Zero profits, but ZA<Z*. 按边际成本定价，但给与补贴Marginal cost pricing with Lump Sum Taxes: Set P=MC, provide Z* at a loss, and finance it with a lump sum tax. p p 问题：这种补贴是否可行？ 公平性考虑：谁使用这种服务或产品？谁受益，谁付费。

Income per week 劳动供给 D 影响因素： • 时间禀赋 (T) • 预算约束, with a price of leisure of $w • 偏好Preferences |Slope| = w E 1 G iii ii Income Leisure 0 Work F time endowment 来源： Rosen i T Hours of leisure per week

收入效应与替代效应 p 税收改变税后 资， 资变化的效应: n n Substitution effect – leisure is relatively less costly after the effective wage is cut, so a person substitutes toward leisure and away from work (↑ leisure). Income effect – The person feels poorer after the effective wage cut and, if leisure is a normal good, the person consumes less of it (↓ leisure).

Income per week 所得税对劳动供给的影响 D 减少劳动供给 |Slope| = w 替代效应>收入效应 H E 1 G G’ 0 |Slope| = (1 -t)w E 2 Hours of i work after tax F I iii ii T Hours of leisure per week Hours of work before tax

Income per week 所得税对劳动供给的影响 增加劳动供给 D 替代效应<收入效应 H E 1 G E 3 K 0 J Hours of work after tax F iii ii i T Hours of leisure per week Hours of work before tax

Wage rate per hour 劳动力供给与税收收入 At wage w, work L 0, and no tax revenue At wage (1 -t 1)w, work L 1, and collect t 1 L 1 in tax revenue. As tax rate gets very high, total tax revenue will eventually fall (to zero). SL w (1 -t 1)w (1 -t 2)w a j k c b d e f (1 -t. A)w (1 -t 3)w h i L 3 LA L 2 L 1 L 0 Hours per week

Tax revenue 税率与税收收入 – Laffer Curve t 1 t 2 t. A t 3 Tax rate