The demand schedule for a product is shown below. Use the information in the tabe to answer the question that follows;
| price ($) | 5 | 10 | 15 | 20 | 25 | 30 |
| Quantity ($) | 60 | 50 | 40 | 30 | 20 | 10 |
(a) Calculate the total revenue at each price.
(b) calculate the total revenue at each price
(i) $5 to $10
(ii) $250 to $30
(c) classify the elasticities calculated in (b) above
(d) What is the relationship between the total revenue and elasticity coefficient calculated in (b)(i) and (ii)
Explanation
(a) Total Revenue = Price x Quantity
TR1 = $5.00 x 60 = $300.00
TR2 = $10.00 x 50 = $500.00
TR3 = $15.00 x 40 = $600.00
TR4 = $20.00 x 30 = $600.00
TR5 = $25.00 x 20 = $500.00
TR6 = $30.00 x 10 = $300.00
(b) (i) When price changes from $5.00 to $10.00
P1 = $5.00 Q1 = 60
P2 = $10.00 Q2 = 50
ฮ P = $5.00 ฮQ = -10
Therefore, price elasticity of demand;
= \(\frac{\bigtriangleup Q}{Q} \times \frac{P} {\bigtriangleup P}\)
= \(\frac{-10}{60} \times \frac{5}{5}\)
= | -0.16| OR |-0.17 |
OR
(ii) When price change from $25.00 to $30.00
P\(_{1}\) = $25.00, Q\(_{1}\) = 20
P\(_{2}\) = $30.00, Q\(_{2}\) = 10
\(\bigtriangleup\)P = $5.00 \(\bigtriangleup\)Q = -10
Therefore, price elasticity of demand
= \(\frac{\bigtriangleup Q}{Q}\) x \(\frac{\bigtriangleup P}{P}\)
= \(\frac{-10}{20} \times \frac{25}{5}\) = | -2.5 |
OR
\(\frac{\%\bigtriangleup \text {quantity demanded}} {\%\bigtriangleup \text {price}}\)
= \(\frac{\bigtriangleup Q}{Q}\) x 100
= \(\frac{-10}{20}\) x 100
\(\frac {\bigtriangleup P}{P}\) x 100
= \(\frac{5}{25}\) x 100