Linear Supply Equation for a Commodity: Solving for Unknown Variables

[wmosley]

Help me figure this one out!

For a certain commodity, the demand equation is given by D= -5p + 5=. At a price of $1, twelve units of the commodity are supplied. If the supply equation is linear and the market price is $4, find the supply equation.

Answer:

For this one I have come up with a formula of:

s= ap+b where p if the varialbe, price, and a,b are constants

s is supply.

I think I have to find a and b but amd not sure.

Can someone help me with figure this one out...

 

[HallsofIvy]

Yes, since you are told that the supply equation is linear, it must be of the form
s= ap+ b. Further, you are told that "At a price of $1, twelve units of the commodity are supplied"- that is, when p= 1, s= 12 so 12= a(1)+ b or a+ b= 1. That means that b= 1- a and the supply equation can be written s= ap+ 1- a. Finally, you are told that the "Market price is $4" which means that the value of p at which the supply and demand equations give s= D is 4. The demand equation is D= -5p + 5. When p= 4, what is D? Now that you know D, you also know s: s= D. Put that value of s as well as p= 4 into the supply equation and solve for a.

 

[M98Ranger]

Sure, I can help you figure this out! First, let's start by understanding the given information. We know that the demand equation is D= -5p + 5 and the market price is $4. We also know that at a price of $1, twelve units of the commodity are supplied. This means that when p=1, s=12.

Now, let's plug in these values into our formula s=ap+b and solve for a and b. We get:

12=a(1)+b
4=a(4)+b

Solving for a and b, we get a=-2 and b=14. Therefore, the supply equation is:

s=-2p+14

To check if this is correct, let's plug in the market price of $4 into the equation and see if we get the correct supply of 12 units:

s=-2(4)+14
s=8+14
s=22

Since we got the correct supply of 22 units, we can be confident that our supply equation is correct. I hope this helps!