Question

When a local firm sets the price of a premium oil change at $50, the number of oil changes done per week is 15. If the firm sets the price at $56, the number of oil changes drops to 12 per week. What is the equation of the firm’s linear demand curve based on these two data points, with P on the left and Q on the right of the equation?

Answer 1

Q = (-1/2)P + 40

Step-by-step explanation:

To find the equation of the firm's linear demand curve, we can use the slope-intercept form of a linear equation: y = mx + b, where "y" represents the dependent variable, "x" represents the independent variable, "m" represents the slope, and "b" represents the y-intercept.

In this case, we can consider "P" (price) as the independent variable (x) and "Q" (quantity of oil changes) as the dependent variable (y).

We have two data points:

Point 1: (P1, Q1) = ($50, 15)

Point 2: (P2, Q2) = ($56, 12)

To find the slope (m), we can use the formula:

m = (Q2 - Q1) / (P2 - P1)

m = (12 - 15) / ($56 - $50)

m = -3 / 6

m = -1/2

Now we have the slope (m = -1/2).

Next, we need to find the y-intercept (b). We can use either of the data points. Let's use Point 1:

15 = (-1/2)($50) + b

15 = -25 + b

b = 40

Now we have the slope (m = -1/2) and the y-intercept (b = 40).

The equation of the firm's linear demand curve is:

Q = (-1/2)P + 40