Table 5.3
$$\begin{array} { c c c }
& \text { Quantity } & \text { Price } \
\text { Good A } & 100 & \$ 10 \
& 120 & \$ 9 \\
\text { Good B } & 200 & \$ 20 \
& 140 & \$ 35
\end{array}$$
-Refer to Table 5.3,which shows the change in the quantity demanded for Good A and Good B as a result of the change in their price.Use the information to calculate the value of the price elasticity of demand for Good B.
A)?2/3
B)?1/6
C)?1/2
D)?11/17
E)?17/11

Question

Table 5.3
 $$\begin{array} { c c c } 
& \text { Quantity } & \text { Price } \
 \text { Good A } & 100 & \$ 10 \
& 120 & \$ 9 \\
\text { Good B } & 200 & \$ 20 \
& 140 & \$ 35
\end{array}$$
-Refer to Table 5.3,which shows the change in the quantity demanded for Good A and Good B as a result of the change in their price.Use the information to calculate the value of the price elasticity of demand for Good B.
A)?2/3
B)?1/6
C)?1/2
D)?11/17
E)?17/11

Quizplus · Accepted Answer

The price elasticity of demand is calculated using the formula: $$E_d = \frac{\%\ change\ in\ quantity\ demanded}{\%\ change\ in\ price}$$. For Good B, the change in quantity demanded is from 200 to 140 (a decrease of 60), and the change in price is from $20 to $35 (an increase of $15). The percentage change in quantity demanded is $\frac{-60}{200} = -0.3$ or -30%, and the percentage change in price is $\frac{15}{20} = 0.75$ or 75%. Thus, $$E_d = \frac{-0.3}{0.75} = -\frac{3}{10} \div \frac{3}{4} = -\frac{3}{10} \times \frac{4}{3} = -\frac{4}{10} = -\frac{2}{5} = -0.4$$, which is not directly listed. However, the calculation seems to have been misunderstood in the initial explanation. Correctly, for Good B, the elasticity should be calculated as follows: $\Delta Q = -60$, $\Delta P = 15$, initial Q = 200, initial P = 20, so $$E_d = \frac{\Delta Q / Q}{\Delta P / P} = \frac{-60/200}{15/20} = \frac{-3}{10} / \frac{3}{4} = -\frac{3}{10} \times \frac{4}{3} = -\frac{4}{10} = -0.4$$. The correct calculation should consider the formula and the correct interpretation of the data, leading to the elasticity of demand for Good B. Given the options, none directly match the calculated value, suggesting a need to reevaluate the calculation or the interpretation of the options provided. The correct calculation for elasticity, using the midpoint formula for a more accurate measure, is: $$E_d = \frac{(Q_2 - Q_1) / ((Q_2 + Q_1)/2)}{(P_2 - P_1) / ((P_2 + P_1)/2)}$$ $$E_d = \frac{(140 - 200) / (140 + 200)/2}{(35 - 20) / (35 + 20)/2} = \frac{-60 / 170}{15 / 27.5} = \frac{-60 / 170}{15 / 27.5} = \frac{-60}{170} \times \frac{27.5}{15} = \frac{-3}{17} \times \frac{11}{3} = -\frac{11}{17}$$. This indicates a mistake in the initial response and calculation. The correct answer should reflect the proper use of the price elasticity of demand formula, considering the specifics of the question and the options provided.

Table 53 -Refer to Table 5