Let's analyze the implications of the given price elasticity of demand for Sylvan Corporation's synthetic wood sorrel.
Given:
- Price Elasticity of Demand (PED) for synthetic wood sorrel = -0.25
- Price increase = 10%
### A. Impact on Quantity Demanded
Price Elasticity of Demand (PED) formula:
\[ \text{PED} = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}} \]
We know PED = -0.25 and the price change is +10%.
Rearranging the formula to solve for the percentage change in quantity demanded:
\[ \% \text{ change in quantity demanded} = \text{PED} \times \% \text{ change in price} \]
\[ \% \text{ change in quantity demanded} = -0.25 \times 10\% \]
\[ \% \text{ change in quantity demanded} = -2.5\% \]
So, the quantity demanded of synthetic wood sorrel will decrease by 2.5% as a result of the 10% increase in price.
### B. Impact on Sylvan's Revenue
Total Revenue (TR) is calculated as:
\[ \text{TR} = \text{Price} \times \text{Quantity} \]
When the price elasticity of demand is inelastic (where \( |PED| < 1 \)), an increase in price leads to a relatively smaller decrease in quantity demanded. In other words, the percentage drop in quantity demanded is less than the percentage increase in price, so total revenue increases.
Given that the price elasticity of demand is -0.25 (which is inelastic since \( |-0.25| < 1 \)):
- Price increases by 10%
- Quantity demanded decreases by 2.5%
While the quantity demanded decreases, the decrease is relatively small compared to the increase in price. Thus, Sylvan's total revenue will increase.
To summarize:
- The quantity demanded of synthetic wood sorrel will decrease by 2.5%.
- Sylvan's total revenue will increase as a result of the price increase.
1. The sylvan corporation has estimated the price elasticity of demand for synthetic wood sorrel to be -0.25
A, if the price of sylvan wood sorrel increases by 10%, what will happen to the quantity demanded of wood hewers?
B. What will happen to sylvans revenue as a result of the price increases ?
1 answer
1 answer