The demand schedule for a product is shown below. Use the information in the tabe to answer the question that follows; price ($) 5 10 15 20 25 30 Quantity (...
Question 1 Report
The demand schedule for a product is shown below. Use the information in the tabe to answer the question that follows;
| price ($) | 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)
Answer Details
(a) Total revenue \( TR = P \times Q \) at each price.
| Price ($) | Quantity | TR = P × Q ($) |
|---|---|---|
| 5 | 60 | 300 |
| 10 | 50 | 500 |
| 15 | 40 | 600 |
| 20 | 30 | 600 |
| 25 | 20 | 500 |
| 30 | 10 | 300 |
(b) Price elasticity of demand using \( E_d = \dfrac{\%\,\Delta Q}{\%\,\Delta P} \) (ignoring the sign).
(i) $5 to $10: quantity falls 60 to 50.
\[ E_d = \frac{-10/60}{5/5} = \frac{-16.67\%}{100\%} = 0.17 \]
(ii) $25 to $30: quantity falls 20 to 10.
\[ E_d = \frac{-10/20}{5/25} = \frac{-50\%}{20\%} = 2.5 \]
(c) Classification
- (i) \( E_d = 0.17 < 1 \): demand is inelastic.
- (ii) \( E_d = 2.5 > 1 \): demand is elastic.
(d) Relationship between total revenue and elasticity
- Over \$5 to \$10 demand is inelastic, and as price rises total revenue rises (300 to 500). When demand is inelastic, price and total revenue move in the same direction.
- Over \$25 to \$30 demand is elastic, and as price rises total revenue falls (500 to 300). When demand is elastic, price and total revenue move in opposite directions.
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