Answer:
The required equilibrium point is (356.538,58.769)
Step-by-step explanation:
The two points on your demand equation are : (300,104) and (250,144)
Take the number of televisions on y-axis and the price of the television on x-axis
Now, to find the demand equation for the given problem, find slope using the above two points :
![\implies Slope=\frac{144-104}{250-300}\\\\\implies Slope = -\frac{4}{5}=-0.8](https://tex.z-dn.net/?f=%5Cimplies%20Slope%3D%5Cfrac%7B144-104%7D%7B250-300%7D%5C%5C%5C%5C%5Cimplies%20Slope%20%3D%20-%5Cfrac%7B4%7D%7B5%7D%3D-0.8)
And the y - intercept is : y = -0.8x + b
Find the value of b using any point. Let us take (250,144)
144 = -0.8 × 250 + b
⇒ b = 144 + 200
⇒ b = 344
So, the y-intercept is : y = -0.8x + 344
The two points on your supply equation are : (225,88) and (315,68)
Take the number of televisions on y-axis and the price of the television on x-axis
Now, to find the supply equation for the given problem, find slope using the above two points :
![\implies Slope=\frac{68-88}{315-225}\\\\\implies Slope = -\frac{2}{9}](https://tex.z-dn.net/?f=%5Cimplies%20Slope%3D%5Cfrac%7B68-88%7D%7B315-225%7D%5C%5C%5C%5C%5Cimplies%20Slope%20%3D%20-%5Cfrac%7B2%7D%7B9%7D)
And the y - intercept is :
![y = -\frac{2}{9}x + b](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B2%7D%7B9%7Dx%20%2B%20b)
Find the value of b using any point. Let us take (225,88)
![88 = -\frac{2}{9}\times 225 + b\\\\\implies b = 88 + 50\\\\\implies b = 138](https://tex.z-dn.net/?f=88%20%3D%20-%5Cfrac%7B2%7D%7B9%7D%5Ctimes%20225%20%2B%20b%5C%5C%5C%5C%5Cimplies%20b%20%3D%2088%20%2B%2050%5C%5C%5C%5C%5Cimplies%20b%20%3D%20138)
So, the y-intercept is :
![y = -\frac{2}{9}x + 138](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B2%7D%7B9%7Dx%20%2B%20138)
To find the equilibrium point, solve both the y-intercepts of the demand equation and the supply equation :
⇒ x = 356.538 and y = 58.769
Hence, the required equilibrium point is (356.538,58.769)