How Do You Derive a Price-Demand Function from Marginal Revenue?

[c19dale]

I have two problems left that are giving me trouble.

here is the first.
If the marginal revenue(in dollars per unit) for producing x units of a product is given by MR= -0.2x^2 + 3.5x + 17.4 and R(0)=0, find the price demand function p for the product.

If some one could just get me started on the right step, that would be great.

 

[Andrew Mason]

I have two problems left that are giving me trouble.

here is the first.
If the marginal revenue(in dollars per unit) for producing x units of a product is given by MR= -0.2x^2 + 3.5x + 17.4 and R(0)=0, find the price demand function p for the product.

If some one could just get me started on the right step, that would be great.

Generally speaking, there aren't a lot of economists here, so you will have to explain what the price demand function is. I assume it is some kind of decreasing function (as price increases, demand decreases and vice versa). Is it linear? What is the function R(x)?

AM

 

[wais]

The price-demand function represents the relationship between the price of a product and the demand for that product. It is typically expressed as p(x), where x represents the quantity of the product being sold. In this problem, we are given the marginal revenue function, MR(x)=-0.2x^2+3.5x+17.4, and we need to find the price-demand function.

To find the price-demand function, we can use the fact that marginal revenue is the change in total revenue divided by the change in quantity, or MR=ΔR/Δx. We also know that total revenue is equal to the price of the product multiplied by the quantity sold, or R=p(x)*x.

Using these two equations, we can set up the following equation:

MR=ΔR/Δx
-0.2x^2+3.5x+17.4=(p(x)*x)-R(0)

Since we are given that R(0)=0, we can simplify the equation to:

-0.2x^2+3.5x+17.4=p(x)*x

Now, to find the price-demand function, we need to solve for p(x). We can do this by dividing both sides of the equation by x:

p(x)=(-0.2x^2+3.5x+17.4)/x

This gives us the price-demand function:

p(x)=-0.2x+3.5+17.4/x

Now, to find the price-demand function, we just need to plug in different values for x and solve for p(x). For example, if we want to find the price for 100 units of the product, we would plug in x=100 into our equation:

p(100)=-0.2(100)+3.5+17.4/100
p(100)=$35.5

Therefore, the price-demand function for this product is p(x)=-0.2x+3.5+17.4/x. I hope this helps you get started on solving your problem.