The demand function is given by P= 2400 - 0.5Q. What is the quantity at which the demand is unit-elastic?

The elasticity of demand is given by the formula:

Elasticity = (dQ/dP) * (P/Q)

Where:

• dQ/dP is the derivative of the quantity with respect to price, which is the slope of the demand function.
• P/Q is the ratio of price to 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:

0.5Q = 2400 - P Q = 4800 - 2P

Next, we find the derivative of Q with respect to P:

dQ/dP = -2

Now, we substitute dQ/dP, P, and Q into the elasticity formula:

Elasticity = (-2) * (P / (4800 - 2P))

We want to find the quantity (Q) at which the demand is unit-elastic, which means the elasticity is -1. So, we set the elasticity equal to -1 and solve for P:

-1 = (-2) * (P / (4800 - 2P)) 1 = 2 * (P / (4800 - 2P)) 4800 - 2P = 2P 4800 = 4P P = 1200

Finally, we substitute P = 1200 into the demand function to find Q:

Q = 4800 - 2*1200 = 2400

So, the quantity at which the demand is unit-elastic is 2400 units.