Question about Marginal Functions? p = −0.01q^2 − 0.2q + 8 and p = 0.01r^2 + 0.1r + 3

[a6m0]

Question about Marginal Functions? p = −0.01q^2 − 0.2q + 8 and p = 0.01r^2 + 0.1r + 3

Hi,

The question im trying to solve is

"Suppose the demand and supply curves for a certain commodity are givenby p = −0.01q^2 − 0.2q + 8 and p = 0.01r^2 + 0.1r + 3, respectively, wherep is in dollars and q, r are in thousands of units. If the sum of the marginalunits demanded and supplied is equal to zero, find a simple relationshipbetween q and r"

I was told that to find the marginal supply and demand, we do the same thing as we do with marginal costs and revenue, by finding their derivatives

So my work so far is:

Marginal demand: p=-0.02q-0.2
Marginal supply: p=0.02r+0.1

since their sum is zero:
(-0.02q-0.2)+(0.02r+0.1)=0

0.02r+0.1 = 0.02q+0.2

I dont understand what finding what their relationship means but im guessing we solve for q and r?

r: 0.02r= 0.02q+0.1
r= q+5

q: 0.02q = 0.02r-0.1
q=r-5

My answer looks weird to me, and im not sure if Im even doing what the question is asking.

Could someone tell me if this is what the question is asking for?

Thanks in advance :razz:

 

[JeffM]

It looks good to me. Not sure that it makes any economic sense of course.

 

[Steven G]

find a simple relationshipbetween q and r"

r= q+5

q: 0.02q = 0.02r-0.1
q=r-5

My answer looks weird to me, and im not sure if Im even doing what the question is asking.

Could someone tell me if this is what the question is asking for?

Thanks in advance :razz:

As Jeff said, your answers look good.

When you are asked to find a relationship between q and r you want an equation that involves q and r.

They can look like q + r =10 (or q=10-r) or q= r -5 or q = r/17 etc. The equation needs to show a relationship between q and r

You did not need to write both r= q+5 AND q=r-5

Good work!