The demand equation for the BWS Bluetooth wireless loudspeaker is p=-0.05x+200 where x is the quantity demanded per month and p is the unit price in dollars. Sketch the graph of the demand curve.
How can I start? What points could I plot?
So I am thinking that I can take on this equation 2 ways:
P= -0.05(0)+200 =200 & 0=-0.05x+200=4000
For (4000,200). Would 4000 be the x value and 200 be the y value? And if correct, would 200 go on the y axis and 4000 on the x axis?
Then the question asks "what is the highest price (theoretically) anyone would pay for a BWS wireless loudspeaker?" How would I start solving it there?
choose x and calculate p
p=-0.05x+200
(0,200),(20,199),(100,195),...(4000,0)
makes sense - no one wants it if the price is steep...
when x=1, p=199.95, the highest price when someone actually buys one.
But wouldn't the highest price be 200 when x=0? since when x is 2 and so on the price seems to decrease.
To sketch the graph of the demand curve, you are correct in choosing two points to plot on the graph. Let's start by finding the coordinates for the first point.
Plug in x = 0 into the equation p = -0.05x + 200 to find the value of p:
p = -0.05(0) + 200
p = 0 + 200
p = 200
So the first point you can plot is (0, 200). This means that when the quantity demanded is 0, the price of the loudspeaker is $200.
Now let's find the coordinates for the second point.
Plug in x = 4000 into the equation p = -0.05x + 200 to find the value of p:
p = -0.05(4000) + 200
p = -200 + 200
p = 0
So the second point you can plot is (4000, 0). This means that when the quantity demanded is 4000, the price of the loudspeaker is $0.
To plot these points on the graph, place 200 on the y-axis (vertical axis) and 0 on the x-axis (horizontal axis) for the first point. Then, place 0 on the y-axis and 4000 on the x-axis for the second point.
Now, to determine the highest price (theoretically) anyone would pay for the BWS wireless loudspeaker, we need to find the maximum value of p in the given equation.
Since the coefficient of x is negative (-0.05), the demand equation represents a linear demand curve that slopes downwards. This means that as the quantity demanded increases, the price decreases.
Since the value of x can theoretically increase infinitely, the price can potentially approach infinity as well.
Therefore, there is no highest price anyone would pay for the BWS wireless loudspeaker because it is technically unlimited.
To sketch the graph of the demand curve, you can start by plotting a few points on the coordinate plane using the given equation.
In the demand equation p = -0.05x + 200, x represents the quantity demanded per month, and p represents the unit price in dollars. So, for a specific quantity demanded (x), you can calculate the corresponding unit price (p).
Let's calculate the unit price (p) for a few values of x:
1. When x = 0:
p = -0.05(0) + 200
p = 200
2. When x = 4000:
p = -0.05(4000) + 200
p = 0 - 200 + 200
p = 0
Based on these calculations, you have correctly identified that the point (4000, 200) lies on the demand curve. The x-value represents the quantity demanded (4000 units), while the y-value represents the unit price ($200).
You can plot this point on a graph, with the x-axis representing the quantity demanded and the y-axis representing the unit price. The point (4000, 200) would be plotted with 4000 on the x-axis and 200 on the y-axis.
Now, to determine the highest price (theoretically) anyone would pay for a BWS wireless loudspeaker, you need to think about the demand equation. The coefficient of x in the equation (-0.05) represents the decrease in unit price for each additional unit sold. As quantity demanded (x) increases, the unit price (p) will decrease.
To find the highest price, you can consider the scenario when the quantity demanded is at its lowest, which is zero. Let's calculate the unit price when x = 0:
p = -0.05(0) + 200
p = 200
In this case, the highest price anyone would pay for a BWS wireless loudspeaker (theoretically) is $200.