To determine the effect of a price reduction and an increase in consumption on revenue, we can use a general approach by denoting the initial price and quantity.
Let's denote:
- \( P \): original price of silk
- \( Q \): original quantity consumed
The original revenue \( R \) can be calculated as: \[ R = P \times Q \]
After a 20% decrease in price, the new price \( P' \) becomes: \[ P' = P \times (1 - 0.20) = P \times 0.80 \]
At the same time, the consumption increases by 30%, making the new quantity \( Q' \): \[ Q' = Q \times (1 + 0.30) = Q \times 1.30 \]
Now, we can calculate the new revenue \( R' \): \[ R' = P' \times Q' = (P \times 0.80) \times (Q \times 1.30) = P \times Q \times 0.80 \times 1.30 \]
Now, compute the new revenue: \[ R' = R \times 0.80 \times 1.30 \]
Calculating \( 0.80 \times 1.30 \): \[ 0.80 \times 1.30 = 1.04 \]
Thus, the new revenue \( R' \) is: \[ R' = R \times 1.04 \]
This means the revenue increases. To find the percentage increase in revenue: \[ \text{Percentage Increase} = \left( \frac{R' - R}{R} \right) \times 100 = \left( \frac{R \times 1.04 - R}{R} \right) \times 100 = (1.04 - 1) \times 100 = 0.04 \times 100 = 4% \]
Thus, the revenue increases by 4%.
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