At a unit price of $55, the quantity demanded of a certain commodity is 1000 units. At a unit price of $85, the demand drops to 600. What quantity would be demanded if the commodity was free? (I worked out the problem and came up with the equation -3/40×+130 but I don't know how to find the quantity that would be demanded if the commodity was free)
when the price drops from $85 to $55 ... $30
... the demand increases from 600 to 1000 ... 400 units
$55 to zero is a drop of $55
the change in demand is ... ($55 / $30) * 400 units
the change is added to the demand at the $55 price point
To find the quantity that would be demanded if the commodity was free, you can substitute a unit price of $0 into the equation and solve for the quantity.
Let's use the equation you provided: q = (-3/40)x + 130
When the unit price is $0, we can substitute x = 0 into the equation:
q = (-3/40)(0) + 130
q = 0 + 130
q = 130
Therefore, if the commodity was free, the quantity demanded would be 130 units.
To find the quantity demanded if the commodity was free, we need to determine the demand function that relates the price and the quantity demanded. From the given information, we can assume that the demand function follows a linear relationship.
Let's set up the demand function in the form of a linear equation: Quantity Demanded = m × Price + b
We have two data points to work with:
1. At a unit price of $55, the quantity demanded is 1000 units: (55, 1000)
2. At a unit price of $85, the quantity demanded is 600 units: (85, 600)
To find the slope (m) and the y-intercept (b) in the linear equation, we can use these two data points.
First, calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (600 - 1000) / (85 - 55)
m = -400 / 30
m = -40/3
Now, let's substitute one of the data points and the slope into the linear equation to find the y-intercept (b). Using the point (55, 1000):
1000 = (-40/3) × 55 + b
Next, solve for b:
1000 = -2200/3 + b
b = 15700/3
So, the demand function is:
Quantity Demanded = (-40/3) × Price + 15700/3
To find the quantity demanded when the commodity is free, we need to set the price to $0 and substitute it into the demand function:
Quantity Demanded = (-40/3) × 0 + 15700/3
Quantity Demanded = 15700/3
Therefore, if the commodity was free, the quantity demanded would be approximately 5233.33 units.