Question

A retail chain will buy 900 cordless phones if the price is $40 each and 700 if the price is $60. a wholesaler will supply 550 phones at $30 each and 1250 at $50 each. Assuming that the supply and demand functions are linear, find the market equilibrium point and explain what it means.

Answer 1

Answer:

The point of equilibrium is (40,900).

Step-by-step explanation:

It is given that the supply and demand functions are linear.

From the given information it is noticed that the demand function passing through the points (40,900) and (60,700). The supply function passing through the points (30,550) and (50,1250).

If a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

The demand function is

$y-900=\frac{700-900}{60-40}(x-40)$

$y-900=-10(x-40)$

$y-900=-10x+400$

$y=-10x+1300$                    .... (1)

The demand function is $y=-10x+1300$.

The supply function is

$y-550=\frac{1250-550}{50-30}(x-30)$

$y-550=35(x-30)$

$y-550=35x-1050$

$y=35x-500$                  .... (2)

The supply function is $y=35x-500$.

Equilibrium is the point where the demand and supply are equal.

On solving (1) and (2), we get

$x=40$

$y=900$

Therefore the point of equilibrium is (40,900). It means the retailer can buy 900 phones for $40 each and the wholesaler can sale 900 phones for $40.