Question

Suppose that in a monopoly market, the demand function for a product is given by p = 490 − 0.2x, where x is the number of units and p is the price in dollars.

• Find the instantaneous rate of change of price p with respect to quantity x.
• Find the total revenue function.

Answer 1

To find the instantaneous rate of change of price p with respect to quantity x, take the derivative of the demand function. The total revenue function is obtained by multiplying the price p by the quantity x.

Step-by-step explanation:

To find the instantaneous rate of change of price p with respect to quantity x, we need to find the derivative of the demand function with respect to x. Taking the derivative of p = 490 - 0.2x, we get dp/dx = -0.2. Therefore, the instantaneous rate of change of price p with respect to quantity x is -0.2.

The total revenue function is obtained by multiplying the price p by the quantity x. In this case, the total revenue function is given by R = px = (490 - 0.2x)x = 490x - 0.2x^2.