The supply function is given as Q=-100 10P.Find the elasticity using p...
Elasticity Calculation using Point Method
Given Information:
- Supply Function: Q = -100 + 10P
- Price: P = 15
Calculating Elasticity:
The formula for price elasticity of supply using point method is:
Elasticity = (Percentage change in quantity supplied / Percentage change in price)
Step 1: Calculate Initial Quantity Supplied
Using the supply function, we can calculate the initial quantity supplied at price P=15:
Q = -100 + 10P
Q = -100 + 10(15)
Q = -100 + 150
Q = 50
Step 2: Calculate New Quantity Supplied
To calculate the new quantity supplied, we need to change the price by a small amount. Let's assume the new price is P=16:
Q = -100 + 10P
Q = -100 + 10(16)
Q = -100 + 160
Q = 60
Step 3: Calculate Percentage Change in Quantity Supplied
The percentage change in quantity supplied is:
Percentage change in quantity supplied = ((New Quantity Supplied - Initial Quantity Supplied) / Initial Quantity Supplied) x 100
Percentage change in quantity supplied = ((60 - 50) / 50) x 100
Percentage change in quantity supplied = 20%
Step 4: Calculate Percentage Change in Price
The percentage change in price is:
Percentage change in price = ((New Price - Initial Price) / Initial Price) x 100
Percentage change in price = ((16 - 15) / 15) x 100
Percentage change in price = 6.67%
Step 5: Calculate Elasticity
Using the formula for price elasticity of supply using point method:
Elasticity = (Percentage change in quantity supplied / Percentage change in price)
Elasticity = (20% / 6.67%)
Elasticity = 3
Interpretation of Results:
The elasticity of supply at price P=15 is 3. This means that a 1% increase in price will result in a 3% increase in quantity supplied.