A group of retailers will buy 104 televisions from a wholesaler if the price is $300 and 144 if the price is $250. The wholesaler is willing to supply 88 if the price is $225 and 168 if the price is $315. Assuming the resulting supply and demand functions are linear, find the equilibrium point for the market.
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throwdolbeau throwdolbeau · Answer 1 · 2019-02-25T10:41:17+01:00

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 :

[tex]\implies Slope=\frac{144-104}{250-300}\\\\\implies Slope = -\frac{4}{5}=-0.8[/tex]

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 :

[tex]\implies Slope=\frac{68-88}{315-225}\\\\\implies Slope = -\frac{2}{9}[/tex]

And the y - intercept is :

[tex]y = -\frac{2}{9}x + b[/tex]

Find the value of b using any point. Let us take (225,88)

[tex]88 = -\frac{2}{9}\times 225 + b\\\\\implies b = 88 + 50\\\\\implies b = 138[/tex]

So, the y-intercept is :

[tex]y = -\frac{2}{9}x + 138[/tex]

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)