第5章弾力性

Calculating the Price Elasticity of Supply供給の価格弾力性の計算

Assume that an apartment rents for $650 per month and at that price the landlord rents 10,000 units as Figure 5.3 shows. When the price increases to $700 per month, the landlord supplies 13,000 units into the market. By what percentage does apartment supply increase? What is the price sensitivity?

英語のヒント

図5.3のように、アパートの家賃が月650ドルで、この価格で家主が10,000戸を貸しているとする。家賃が月700ドルへ上がると、市場への供給は13,000戸になる。アパートの供給は何％増えたか。価格への感応度はどれほどか。

賃貸アパートの供給を表す右上がりの直線。 — Figure 5.3図 5.3
We calculate the price elasticity of supply as the percentage change in quantity divided by the percentage change in price.
英語のヒント
供給の価格弾力性は、数量の変化率を価格の変化率で割って計算する。

Using the Midpoint Method,

英語のヒント

中点法を使うと、

\begin{array}{rcl} % change in quantity & = & \frac{13,000 - 10,000}{(13,000 + 10,000)/2} × 100 \\ = & \frac{3,000}{11,500} × 100 \\ = & 26.1 \\ % change in price & = & \frac{$700 - $650}{($700 + $650)/2} × 100 \\ = & \frac{50}{675} × 100 \\ = & 7.4 \\ Price Elasticity of Supply & = & \frac{26.1%}{7.4%} \\ = & 3.53 \end{array}

\begin{array}{rcl} 数量の変化率（％） & = & \frac{13,000 - 10,000}{(13,000 + 10,000)/2} × 100 \\ = & \frac{3,000}{11,500} × 100 \\ = & 26.1 \\ 価格の変化率（％） & = & \frac{$700 - $650}{($700 + $650)/2} × 100 \\ = & \frac{50}{675} × 100 \\ = & 7.4 \\ 供給の価格弾力性 & = & \frac{26.1%}{7.4%} \\ = & 3.53 \end{array}

Again, as with the elasticity of demand, the elasticity of supply is not followed by any units. Elasticity is a ratio of one percentage change to another percentage change—nothing more—and we read it as an absolute value. In this case, a 1% rise in price causes an increase in quantity supplied of 3.5%. The greater than one elasticity of supply means that the percentage change in quantity supplied will be greater than a one percent price change. If you're starting to wonder if the concept of slope fits into this calculation, read the following Clear It Up box.

英語のヒント

需要の弾力性と同様、供給の弾力性にも単位は付かない。弾力性は、ある変化率と別の変化率の比にすぎず、絶対値として読む。この場合、1％の値上がりが供給量を3.5％増やす。供給の弾力性が1より大きいことは、供給量の変化率が価格の1％の変化より大きいことを意味する。傾きの概念がこの計算とどう関係するか気になったら、次の「疑問を解く」を読もう。

Is the elasticity the slope?弾力性は傾きなのか

It is a common mistake to confuse the slope of either the supply or demand curve with its elasticity. The slope is the rate of change in units along the curve, or the rise/run (change in y over the change in x). For example, in Figure 5.2, at each point shown on the demand curve, price drops by $10 and the number of units demanded increases by 200 compared to the point to its left. The slope is –10/200 along the entire demand curve and does not change. The price elasticity, however, changes along the curve. Elasticity between points A and B was 0.45 and increased to 1.47 between points G and H. Elasticity is the percentage change, which is a different calculation from the slope and has a different meaning.

英語のヒント

供給曲線や需要曲線の傾きと弾力性を混同するのは、よくある間違いである。傾きは、曲線に沿った数量単位での変化率、つまり縦の変化を横の変化で割った値、yの変化÷xの変化である。例えば図5.2では、需要曲線上の各点は、その左の点と比べて価格が10ドル下がり、需要量が200増える。需要曲線全体で傾きは−10/200であり、変わらない。しかし価格弾力性は曲線に沿って変わる。AとBの間では0.45、GとHの間では1.47へ増えた。弾力性は百分率の変化を使うため、傾きとは計算も意味も違う。

When we are at the upper end of a demand curve, where price is high and the quantity demanded is low, a small change in the quantity demanded, even in, say, one unit, is pretty big in percentage terms. A change in price of, say, a dollar, is going to be much less important in percentage terms than it would have been at the bottom of the demand curve. Likewise, at the bottom of the demand curve, that one unit change when the quantity demanded is high will be small as a percentage.

英語のヒント

需要曲線の上端では、価格が高く需要量が少ない。そのため、需要量の小さな変化、例えば1単位でも、百分率で見ればかなり大きい。価格の1ドルの変化は、曲線の下端の場合に比べ、百分率での重要性がはるかに小さい。同様に、需要量が多い曲線の下端では、1単位の数量変化は百分率では小さくなる。

Thus, at one end of the demand curve, where we have a large percentage change in quantity demanded over a small percentage change in price, the elasticity value would be high, or demand would be relatively elastic. Even with the same change in the price and the same change in the quantity demanded, at the other end of the demand curve the quantity is much higher, and the price is much lower, so the percentage change in quantity demanded is smaller and the percentage change in price is much higher. That means at the bottom of the curve we'd have a small numerator over a large denominator, so the elasticity measure would be much lower, or inelastic.

英語のヒント

したがって、需要曲線の一方の端では、価格の小さな変化率に対して需要量の変化率が大きく、弾力性は大きい。つまり、需要は比較的弾力的である。価格と需要量の変化の絶対量が同じでも、もう一方の端では数量がはるかに多く、価格がはるかに低い。そのため、数量の変化率は小さく、価格の変化率は大きくなる。曲線の下端では、小さい分子を大きい分母で割るため、弾力性はかなり小さく、非弾力的になる。

As we move along the demand curve, the values for quantity and price go up or down, depending on which way we are moving, so the percentages for, say, a $1 difference in price or a one unit difference in quantity, will change as well, which means the ratios of those percentages and hence the elasticity will change.

英語のヒント

需要曲線に沿って動くと、進む方向によって数量と価格の値が増減する。そのため、例えば価格1ドルの差や数量1単位の差が占める百分率も変わる。その百分率の比も変わり、したがって弾力性も変わる。

Key Concepts and Summary重要概念とまとめ

Price elasticity measures the responsiveness of the quantity demanded or supplied of a good to a change in its price. We compute it as the percentage change in quantity demanded (or supplied) divided by the percentage change in price. We can describe elasticity as elastic (or very responsive), unit elastic, or inelastic (not very responsive). Elastic demand or supply curves indicate that quantity demanded or supplied respond to price changes in a greater than proportional manner. An inelastic demand or supply curve is one where a given percentage change in price will cause a smaller percentage change in quantity demanded or supplied. A unitary elasticity means that a given percentage change in price leads to an equal percentage change in quantity demanded or supplied.

英語のヒント

価格弾力性は、財の需要量や供給量が、その価格の変化にどれほど反応するかを測る。需要量または供給量の変化率を、価格の変化率で割って計算する。弾力的、つまり反応が大きい場合、単位弾力的な場合、非弾力的、つまり反応が小さい場合がある。弾力的な需要曲線や供給曲線では、数量は価格変化を上回る割合で反応する。非弾力的な曲線では、ある割合の価格変化に対して、数量の変化率はそれより小さい。単位弾力性では、価格と数量が同じ割合で変わる。