Answer:
(275,122)
When the price will be $275, the quantity will be 122 televisions.
Step-by-step explanation:
We have been given that a group of retailers will buy 104 televisions from a wholesaler if the price is $300 and 144 if the price is $250.
As the quantity of televisions depends on price of televisions, so our demand curve will pass through points (300,104) and (250,144).
Let us find slope of demand line using slope formula.
, where,
,
,
![x_2-x_1=\text{Difference between same x-coordinates of two y-coordinates}](https://tex.z-dn.net/?f=x_2-x_1%3D%5Ctext%7BDifference%20between%20same%20x-coordinates%20of%20two%20y-coordinates%7D)
Upon substituting coordinates of our given points in slope formula we will get,
![m=\frac{104-144}{300-250}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B104-144%7D%7B300-250%7D)
![m=\frac{-40}{50}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-40%7D%7B50%7D)
Let us substitute
coordinates of point (250,144) in slope intercept form of equation (
).
![144=-\frac{4}{5}*250+b](https://tex.z-dn.net/?f=144%3D-%5Cfrac%7B4%7D%7B5%7D%2A250%2Bb)
![144=-4*50+b](https://tex.z-dn.net/?f=144%3D-4%2A50%2Bb)
![144=-200+b](https://tex.z-dn.net/?f=144%3D-200%2Bb)
![344=b](https://tex.z-dn.net/?f=344%3Db)
Upon substituting
and
we will get equation of our demand line as:
Similarly we will find the equation of supply line using points (225,88) and (315,168).
![m=\frac{168-88}{315-225}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B168-88%7D%7B315-225%7D)
![m=\frac{80}{90}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B80%7D%7B90%7D)
![m=\frac{8}{9}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B8%7D%7B9%7D)
Let us substitute
and coordinates of point (225,88) in slope intercept form of equation (
).
![88=\frac{8}{9}*225+b](https://tex.z-dn.net/?f=88%3D%5Cfrac%7B8%7D%7B9%7D%2A225%2Bb)
![88=8*25+b](https://tex.z-dn.net/?f=88%3D8%2A25%2Bb)
![88=200+b](https://tex.z-dn.net/?f=88%3D200%2Bb)
![88-200=200-200+b](https://tex.z-dn.net/?f=88-200%3D200-200%2Bb)
![-112=b](https://tex.z-dn.net/?f=-112%3Db)
Upon substituting
and
we will get equation of our supply line as:
![y=\frac{8}{9}x-122](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B8%7D%7B9%7Dx-122)
Let us equate both lines to find the point where both lines intersect.
![-\frac{4}{5}x+344=\frac{8}{9}x-122](https://tex.z-dn.net/?f=-%5Cfrac%7B4%7D%7B5%7Dx%2B344%3D%5Cfrac%7B8%7D%7B9%7Dx-122)
![-\frac{4}{5}x-\frac{8}{9}x+344=\frac{8}{9}x-\frac{8}{9}x-122](https://tex.z-dn.net/?f=-%5Cfrac%7B4%7D%7B5%7Dx-%5Cfrac%7B8%7D%7B9%7Dx%2B344%3D%5Cfrac%7B8%7D%7B9%7Dx-%5Cfrac%7B8%7D%7B9%7Dx-122)
![-\frac{4}{5}x-\frac{8}{9}x+344=-122](https://tex.z-dn.net/?f=-%5Cfrac%7B4%7D%7B5%7Dx-%5Cfrac%7B8%7D%7B9%7Dx%2B344%3D-122)
![-\frac{4}{5}x-\frac{8}{9}x+344-344=-122-344](https://tex.z-dn.net/?f=-%5Cfrac%7B4%7D%7B5%7Dx-%5Cfrac%7B8%7D%7B9%7Dx%2B344-344%3D-122-344)
Let us have a common denominator.
![-\frac{4*9}{5*9}x-\frac{8*5}{9*5}x=-466](https://tex.z-dn.net/?f=-%5Cfrac%7B4%2A9%7D%7B5%2A9%7Dx-%5Cfrac%7B8%2A5%7D%7B9%2A5%7Dx%3D-466)
![-\frac{36}{45}x-\frac{40}{45}x=-466](https://tex.z-dn.net/?f=-%5Cfrac%7B36%7D%7B45%7Dx-%5Cfrac%7B40%7D%7B45%7Dx%3D-466)
![\frac{-36-40}{45}x=-466](https://tex.z-dn.net/?f=%5Cfrac%7B-36-40%7D%7B45%7Dx%3D-466)
![\frac{-76}{45}x=-466](https://tex.z-dn.net/?f=%5Cfrac%7B-76%7D%7B45%7Dx%3D-466)
![\frac{-76}{45}*\frac{45}{-76}x=-466*\frac{45}{-76}](https://tex.z-dn.net/?f=%5Cfrac%7B-76%7D%7B45%7D%2A%5Cfrac%7B45%7D%7B-76%7Dx%3D-466%2A%5Cfrac%7B45%7D%7B-76%7D)
![x=466*\frac{45}{76}](https://tex.z-dn.net/?f=x%3D466%2A%5Cfrac%7B45%7D%7B76%7D)
![x=6.1315789473684211*45](https://tex.z-dn.net/?f=x%3D6.1315789473684211%2A45)
Let us substitute x=275 in any of our equation to solve for y.
![y=-\frac{4}{5}*275+344](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B4%7D%7B5%7D%2A275%2B344)
![y=-4*55+344](https://tex.z-dn.net/?f=y%3D-4%2A55%2B344)
![y=-220+344](https://tex.z-dn.net/?f=y%3D-220%2B344)
![y=122](https://tex.z-dn.net/?f=y%3D122)
Therefore, the equilibrium point for the market will be (275,122).