No, the price elasticity of demand (PED) is not the same along a linear demand curve.不，需求价格弹性 (PED) 沿着线性需求曲线并不相同。

A linear demand curve has a constant slope, which means the change in quantity demanded per unit change in price remains constant. However, PED, which measures the percentage change in quantity demanded relative to the percentage change in price, varies along the curve.线性需求曲线具有恒定的斜率，这意味着每单位价格变化的需求量变化保持恒定。然而，衡量需求量相对于价格变化百分比的 PED 沿曲线变化。

Here's why it changes:这就是它改变的原因：

• At higher prices and lower quantities (upper part of the demand curve), the PED is relatively elastic. Small changes in price result in larger percentage changes in quantity demanded because the base quantity is smaller.在较高价格和较低数量（需求曲线的上部）的情况下，PED 相对有弹性。由于基本数量较小，价格的微小变化会导致需求量的百分比变化较大。
• At lower prices and higher quantities (lower part of the demand curve), the PED becomes inelastic. Here, changes in price lead to smaller percentage changes in quantity demanded because the base quantity is larger.当价格较低且数量较多时（需求曲线的下部），PED 变得缺乏弹性。在这里，价格变化导致需求量百分比变化较小，因为基本数量较大。

At the midpoint of a linear demand curve, PED is typically unit elastic, meaning a 1% change in price results in a 1% change in quantity demanded.在线性需求曲线的中点，PED 通常具有单位弹性，这意味着价格变化 1% 会导致需求量变化 1%。

Certainly! Here’s a table where we calculate the Price Elasticity of Demand (PED) using the endpoint method for each interval along a linear demand curve where price goes from 0 to 6, and quantity goes from 6 to 0.当然！在下表中，我们使用端点法计算线性需求曲线上每个区间的需求价格弹性 (PED)，其中价格从 0 到 6，数量从 6 到 0。

Step-by-Step Explanation分步说明

1. Endpoint Method Formula for PED:PED 终点法公式：

   $$\text{PED} = \frac{\left( \frac{Q_2 - Q_1}{Q_2 + Q_1} \right)}{\left( \frac{P_2 - P_1}{P_2 + P_1} \right)}$$

   where $Q_1$ and $Q_2$ are the initial and final quantities, and $P_1$ and $P_2$ are the initial and final prices in each interval.在哪里 $Q_1$ 和 $Q_2$ 是初始数量和最终数量，并且 $P_1$ 和 $P_2$ 是每个区间的初始价格和最终价格。

2. Intervals: We’ll calculate PED for each interval as the price decreases from 6 to 0 and the quantity increases from 0 to 6.间隔：当价格从 6 减少到 0、数量从 0 增加到 6 时，我们将计算每个间隔的 PED。

Table: PED Calculation Using Endpoint Method表：使用端点法的 PED 计算

Analysis of the Table表中分析

• Higher Prices (Intervals 1-2): PED is greater than 1, indicating elastic demand.价格较高（区间 1-2） ：PED 大于 1，表明需求富有弹性。
• Midpoint: Around intervals 2-3, the PED nears 1, suggesting unit elasticity.中点：在区间 2-3 附近，PED 接近 1，表明单位弹性。
• Lower Prices (Intervals 4-6): PED drops below 1, indicating inelastic demand.较低的价格（区间 4-6） ：PED 降至 1 以下，表明需求缺乏弹性。

This confirms that on a linear demand curve, PED is high (elastic) at the top, unit elastic in the middle, and low (inelastic) at the bottom.这证实了在线性需求曲线上，PED 在顶部较高（有弹性），在中间具有单位弹性，在底部较低（无弹性）。

You are absolutely correct! Let’s clarify this:你是绝对正确的！让我们澄清一下：

On a linear demand curve, the Price Elasticity of Demand (PED) behaves differently at the two endpoints:在线性需求曲线上，需求价格弹性 (PED) 在两个端点处表现不同：

1. Intersection with the Price Axis (Vertical Intercept):与价格轴的交点（垂直截距） ：

   • At this point, price is at its maximum, and quantity demanded is zero.此时，价格处于最高点，需求量为零。
   • PED here is negative infinity because a very small percentage change in price would lead to a large percentage change in quantity demanded (from zero to some positive amount).这里的 PED 是负无穷大，因为价格的一个非常小的百分比变化将导致需求量的一个大的百分比变化（从零到某个正数）。

2. Intersection with the Quantity Axis (Horizontal Intercept):与数量轴的交点（水平截距） ：

   • At this point, quantity is at its maximum, and price is zero.此时，数量达到最大，价格为零。
   • PED here is zero because any percentage change in price from zero has no impact on quantity demanded (which remains at its maximum level).这里的 PED为零，因为价格从零开始的任何百分比变化都不会影响需求量（仍保持在最高水平）。

In summary:总之：

• Top of the Demand Curve (Price Axis Intercept): PED is $-\infty$ (perfectly elastic).需求曲线顶部（价格轴截距） ：PED 是 $-\infty$ （完全有弹性）。
• Bottom of the Demand Curve (Quantity Axis Intercept): PED is $0$ (perfectly inelastic).需求曲线底部（数量轴截距） ：PED 是 $0$ （完全无弹性）。

This highlights that along a linear demand curve:这凸显了沿着线性需求曲线：

• PED decreases from negative infinity to zero as we move from the price axis (high price, low quantity) down to the quantity axis (low price, high quantity).当我们从价格轴（高价格，低数量）向下移动到数量轴（低价格，高数量）时，PED 从负无穷减小到零。