# Need help finishing problem

need help finishing problem!!

For a certain commodity, the deman equation is given by D= -5p + 50. 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.

I know that the supply equation is linear, it must be of the form
s= ap+ b. I also know 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, its says 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? I know what D equals. I also know s: s= D. I'm just not sure how put that value of s as well as p= 4 into the supply equation and solve for a. Can someone help!

Last edited:

Gokul43201
Staff Emeritus
Gold Member
Can you make sure you copied the question down correctly (especially, the demand curve) ? At a market price of $4, the demand would be negative (-15), and that's not sensible. -------------------------------------------------------------------------------- I edited the problem, everything should read correctly now.. Gokul43201 Staff Emeritus Science Advisor Gold Member wmosley said: For a certain commodity, the deman equation is given by D= -5p + 50. 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. I know that the supply equation is linear, it must be of the form s= ap+ b. I also know 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.
You mean a+b=12 or b=12-a, or S = ap + 12 - a

That means that b= 1- a and the supply equation can be written s= ap+ 1- a. Finally, its says 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.
Correct.

The demand equation is D= -5p + 5. When p= 4, what is D?
You mean D = -5p + 50, according to your correction. So at p=4, D = -20+50 = 30.

I know what D equals. I also know s: s= D.
At p=4, S=D, and D=30, so S=30.

I'm just not sure how put that value of s as well as p= 4 into the supply equation and solve for a. Can someone help!
Now use S(4) = 30 in the equation for the supply curve.
Again, S = ap + 12 - a = 4a + 12 - a = 30
Or, 3a + 12 = 30.

This gives you 'a', from which you get the complete supply curve equation.