A company that supplies water to a city faces a market demand curve of P = 161-3q. At what price does the company maximise total revenue?

To find the price that maximizes total revenue, we first need to understand that total revenue is maximized at the point where the price elasticity of demand is unitary (i.e., equal to 1). This occurs at the midpoint of the linear demand curve.

Step 1: Find the quantity where demand becomes zero (q=0) Setting P = 0 in the demand equation gives us:

0 = 161 - 3q 3q = 161 q = 161/3 = 53.67

Step 2: Find the midpoint quantity The midpoint quantity is half of the quantity where demand becomes zero:

Midpoint quantity = 53.67/2 = 26.835

Step 3: Substitute the midpoint quantity into the demand equation to find the price Substituting q = 26.835 into the demand equation P = 161 - 3q gives us:

P = 161 - 3*26.835 = 80.495

So, the company maximizes total revenue when the price is approximately $80.50.