# Demand Function and Rate of Change

1. May 13, 2013

### TrendyBendy

1. The problem statement, all variables and given/known data
The demand function for a certain product is given by pq=4000, where p is the price charged per item and q is the quantity which can be sold at that price. If the product currently sells for $3.50 per item, what would be the rate of change of quantity over time if the rate of change of price over time is$0.50?

2. Relevant equations
pq=4000

3. The attempt at a solution
Honestly, the getting started part is what is tripping me up. The equation looks simple enough but TOO simple. It's throwing me off! I know I need to find the derivative, so I'm thinking (3.50)q=4000, but I'm so unsure!!

Last edited by a moderator: May 13, 2013
2. May 13, 2013

### milesyoung

If you saw an equation like:
p(t)q(t) = K

would you be able to find dq/dt?

3. May 13, 2013

### TrendyBendy

I guess. That does look a lot more familiar than what my equation looks like. But there is no t, so I feel lost.

4. May 13, 2013

### milesyoung

You can let p and q be functions of any variable you'd like. Choose what makes sense for the problem you're given.

Do you know the product or chain rule, or both?

5. May 13, 2013

### TrendyBendy

But that's just the thing. I've searched everywhere, even my textbook, and nothing looks like this demand function. Even in my book the functions that it asks me to solve have a more comprehensive function, like : "the demand function for a certain product is given by p=50,000-q/25,000, fin the marginal revenue of q=10,000 units and p is in dollars." This makes more sense to me, I can work with this. But this function, pq=4000 just doesn't look right. I don't "know" the product or chain rule very well. I can follow steps, but none of this is sticking in my brain very well!

6. May 13, 2013

### milesyoung

I'm far from an expert in economics, so I just see: Price goes up → demand goes down and vice versa. It might be a poor model compared to what you're used to but that doesn't mean we can't figure out the math problem you posted.

Try finding the derivative with respect to t of both sides of:
p(t)q(t) = K

where K is a constant.

7. May 13, 2013

### Ray Vickson

Have you taken calculus? If so, this is an easy problem: you are given that p and q depend on t (t = time) and you are given dp/dt = 0.5 at the point p = p(t) = 3.5. Remember, p and q are related through p*q = 4000; that is, you need to preserve the relationship p(t)*q(t) = 4000 for all t.

Things will be a bit more challenging if you have not had calculus. We cannot guess what you know; you need to tell us.

8. May 13, 2013

### TrendyBendy

I am taking calculus right now, and this is one of my homework problems, so that is why I am struggling. I'm trying to understand. I get super confused in word problems, but now I see time. Thanks. I'm going to try this out and see what happens.

9. May 13, 2013

### TrendyBendy

I'm so confused and lost. Can someone please just tell me the equation I need to start with? I'm racking my brain. I need to see what steps I need to take. Now I've got all the components but have no clue as to where to put everything.

10. May 13, 2013

### milesyoung

As I said, you could start by finding the derivative with respect to t of both sides of:
p(t)q(t) = K

That would give you an equation with dq/dt in it for you to isolate. You would need to apply the product rule.

Alternatively, isolate q(t) first and use the chain rule to find dq/dt.