the demand function, P=20-0.5Q Determine the price elasticity of demand when P=2
To determine the price elasticity of demand when P = 2, we need to calculate the absolute value of the derivative of the demand function with respect to price (dQ/dP), multiplied by the price (P), and then divide it by the quantity (Q).
First, let's differentiate the demand function with respect to price (P):
dQ/dP = -0.5
Next, let's substitute P = 2 into the demand function and solve for Q:
P = 20 - 0.5Q
2 = 20 - 0.5Q
0.5Q = 18
Q = 18 / 0.5
Q = 36
Now, let's calculate the price elasticity of demand:
Price elasticity of demand = (|dQ/dP| * P) / Q
|dQ/dP| = |(-0.5)| = 0.5 (taking the absolute value)
Price elasticity of demand = (0.5 * 2) / 36
Price elasticity of demand = 0.1 / 36
Price elasticity of demand ≈ 0.0028
Therefore, when the price is $2, the price elasticity of demand is approximately 0.0028. This means that the demand is inelastic, indicating a small change in quantity demanded in response to a change in price.