The demand function is given by P= 2400 - 0.5Q. What is the quantity at which the demand is unit-elastic?
Question
The demand function is given by P= 2400 - 0.5Q. What is the quantity at which the demand is unit-elastic?
Solution
The elasticity of demand is given by the formula:
Elasticity = (dQ/dP) * (P/Q)
Where:
- dQ/dP is the derivative of the demand function with respect to price
- P is the price
- Q is the quantity
The demand function is given by P = 2400 - 0.5Q.
First, we need to rearrange this equation to express Q in terms of P:
Q = 4800 - 2P
Next, we differentiate Q with respect to P to get dQ/dP:
dQ/dP = -2
Now, we substitute dQ/dP, P, and Q into the elasticity formula and set it equal to -1 (since we're looking for the point where demand is unit-elastic):
-1 = (-2) * (P/(4800 - 2P))
Solving this equation for P gives:
P = 2400
Substituting P = 2400 back into the demand function gives:
Q = 4800 - 2*2400 = 0
So, the quantity at which demand is unit-elastic is 0.
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