Hello
I was wondering if someone could help me with this.
P=Price
Q=Quantity
TR = Total Revenue
Price ($) Quantity
7 0
6 100
5 200
4 300
3 400
2 500
1 600
0 700
Total Revenue = P X Q
We assume a linear relationship.
They said that they know the demand curve is Q = 700 - 100P
How did they get that? Do you have to do a graph to figure that out? How do you get that based on looking at the data?
Thanks in advance.
Draw a graph and you will see that it is true. Each drop in price (P) of one unit results in an increase in quantity (Q) of 100.
Hello!
To determine the demand curve equation, you do not necessarily need a graph. You can derive it using the given data and the formula for total revenue.
First, let's calculate the total revenue for each price and quantity combination:
For P = 7, Q = 0, TR = 7 x 0 = 0
For P = 6, Q = 100, TR = 6 x 100 = 600
For P = 5, Q = 200, TR = 5 x 200 = 1000
For P = 4, Q = 300, TR = 4 x 300 = 1200
For P = 3, Q = 400, TR = 3 x 400 = 1200
For P = 2, Q = 500, TR = 2 x 500 = 1000
For P = 1, Q = 600, TR = 1 x 600 = 600
For P = 0, Q = 700, TR = 0 x 700 = 0
Now, let's analyze the data:
We can observe that when the quantity is at its maximum (Q = 700), the price is at its minimum (P = 0), giving us a TR of 0, which means there is no revenue (since P x Q = 0).
As the price increases from 0 to 7, the quantity demanded decreases from 700 to 0.
Based on this pattern, we can deduce that the demand curve is downward sloping, indicating an inverse relationship between price and quantity demanded.
Now, let’s identify the equation for the demand curve using the given information: Q = 700 - 100P.
This equation suggests that when the price (P) is zero, the quantity demanded (Q) is maximum (700). As the price increases, the quantity demanded decreases linearly with a slope of -100. The constant term (700) represents the quantity demanded when the price is zero.
Hence, by analyzing the given data, we can determine the equation for the demand curve without necessarily plotting it on a graph.