Question

For a certain commodity the supply equation is given by S = 2p + 5 At a price of $1, there is a demand for 19 units of the commodity. If the demand equation is linear and the market price is $3, find the demand equation.

Answer 1

Answer:

The demand equation is: D=-4p+23

Step-by-step explanation:

To get started, we should keep in mind that the market price (p=3) occurs when supply equals demand ,therefore when p=3

S=2(3)+5=11

Thus, when p=3 D=11 and, according to the problem  when p=1 D=19.

We already know two points on the demand curve. Great!

The demand equation is linear, so it has form D=bp+c.

The variable b is the slope of  the demand linear equation . It can be computed through the formula

$b=\frac{y2-y1}{x2-x1}$.  equation 1

Substituting the two points (3,11) and (1,19) on equation 1.

$b=\frac{19-11}{1-3} =\frac{8}{-2}$

b=-4

Now we can find the value of  intercept of the demand equation c trough point-slope form y-y1=b(x-x1).

We can use any of the points. Let's take (3,11) and write in point-slope :

y-11=-4(x-3)

y=-4x+11+12

y=-4x+23

Rewrite the linear equation according our variables D and p

D=-4P+23

Finally we found the demand equation !