您说:
is the PED same along the linear demand curve?沿线性需求曲线的 PED 是否相同?
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 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。
Endpoint Method Formula for PED:PED 终点法公式:
PED=(P2+P1P2−P1)(Q2+Q1Q2−Q1)where Q1 and Q2 are the initial and final quantities, and P1 and P2 are the initial and final prices in each interval.在哪里 Q1 和 Q2 是初始数量和最终数量,并且 P1 和 P2 是每个区间的初始价格和最终价格。
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。
Interval间隔 | Price (P)价格 ( P ) | Quantity (Q)数量 ( Q ) | P1 | P2 | Q1 | Q2 | PED CalculationPED计算 | PED ValuePED值 |
---|---|---|---|---|---|---|---|---|
1 | 6 to 56 至 5 | 0 to 10 到 1 | 6 | 5 | 0 | 1 | (5−6)/(5+6)(1−0)/(1+0) | 2.2 |
2 | 5 to 45 至 4 | 1 to 21 至 2 | 5 | 4 | 1 | 2 | (4−5)/(4+5)(2−1)/(2+1) | 1.4 |
3 | 4 to 34 至 3 | 2 to 32 至 3 | 4 | 3 | 2 | 3 | (3−4)/(3+4)(3−2)/(3+2) | 0.86 |
4 | 3 to 23比2 | 3 to 43至4 | 3 | 2 | 3 | 4 | (2−3)/(2+3)(4−3)/(4+3) | 0.57 |
5 | 2 to 12比1 | 4 to 54 至 5 | 2 | 1 | 4 | 5 | (1−2)/(1+2)(5−4)/(5+4) | 0.33 |
6 | 1 to 01对0 | 5 to 65 至 6 | 1 | 0 | 5 | 6 | (0−1)/(0+1)(6−5)/(6+5) | 0.18 |
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:
Intersection with the Price Axis (Vertical Intercept):与价格轴的交点(垂直截距) :
Intersection with the Quantity Axis (Horizontal Intercept):与数量轴的交点(水平截距) :
In summary:总之:
This highlights that along a linear demand curve:这凸显了沿着线性需求曲线: