The quantity demanded for a certain brand of portable CD players is 200 units when the unit price is set at $90. The quantity demanded is 1,200 units when the unit price is $40. Find the demand equation.
I'm leaning toward d, but I'm not sure.
a. p = - 0.05x + 100
b. p = - 0.04x + 100
c. p = - 0.05x + 90
d. p = - 0.04x + 90
Thank you
To find the demand equation, we need to determine the relationship between the quantity demanded and the unit price. Let's use the given information to calculate the slope of the demand equation.
Given data points:
Price (p1) = $90, Quantity (x1) = 200
Price (p2) = $40, Quantity (x2) = 1200
The slope (m) of the demand equation can be calculated using the formula:
m = (p2 - p1) / (x2 - x1)
Substituting the values:
m = (40 - 90) / (1200 - 200)
= (-50) / (1000)
= -0.05
Now that we have the slope, we can write the demand equation in the form:
p = mx + b
where p represents the price, x represents the quantity, m is the slope, and b is the y-intercept.
We have the slope (m = -0.05), so we just need to find the y-intercept (b). Let's substitute one of the data points into the equation and solve for b:
p = mx + b
90 = -0.05 * 200 + b
90 = -10 + b
b = 90 + 10
b = 100
Therefore, the demand equation is:
p = -0.05x + 100
So, the correct answer is a. p = -0.05x + 100.
To find the demand equation, we can use the given information about the quantity demanded at different prices. We can assume that the demand equation follows a linear relationship between the quantity demanded (x) and the unit price (p).
Let's start by finding the slope of the demand equation. The slope represents the rate at which the quantity demanded changes with respect to the unit price. We can use the formula:
slope = (change in y) / (change in x)
In this case, the change in quantity demanded is 1200 - 200 = 1000 units, and the change in unit price is $40 - $90 = -$50. Therefore, the slope is:
slope = (1000 units) / (-$50) = -20 units per dollar
Now that we have the slope, we can use the point-slope form of a linear equation to find the demand equation. The point-slope form is given by the equation:
y - y1 = m(x - x1)
where y represents the unit price (p), x represents the quantity demanded, m represents the slope, and (x1, y1) are the coordinates of a point on the line (in this case, the coordinates can be either of the given quantity-price pairs).
Let's use the first given quantity-price pair (200 units, $90), and plug in the values into the point-slope form:
p - $90 = -20 (x - 200)
Simplifying the equation, we get:
p - $90 = -20x + 4000
p = -20x + 4000 + $90
p = -20x + $4090
Comparing this equation with the options given:
a. p = -0.05x + $100
b. p = -0.04x + $100
c. p = -0.05x + $90
d. p = -0.04x + $90
We can see that the correct demand equation is:
d. p = -0.04x + $90
Therefore, the correct answer is option (d).
hmmmm. It asks for demand equation, but gives answers in Inverse Price equation.
Demand equation:
demand=b-a*Price
Inverse demand equation:
P=Q/a+b where Q is demand, P price, a and b are constants.
Data
40=1200/a + b
90=200/a + b
subtract second from first
-50=1000/a
a= -20
then second equation with a
90=200/20 + b
b=80
Inverse demand equation then is
p=Q/-20 +90
p=-.05Q+90