Expert: Ahmed Salami - 7/5/2010

Question
QUESTION: Hello. I'm helping someone on Yahoo! Answers with a question:

If C(x) = 19000 + 400x - 1.6x^2 + 0.004x^3 is the cost function and p(x) = 1600 - 7x?
If C(x) = 19000 + 400x - 1.6x^2 + 0.004x^3 is the cost function and p(x) = 1600 - 7x is the demand function, find the production level that will maximize profit. #Hint: If the profit is maximized, then the marginal revenue equals the marginal cost.)

I'm not asking you to help me solve it, I'd like for you to show me how to determine the revenue function. If I know what the revenue function is then I can proceed. I'm trying to figure this out and am getting confused-please help me out. Thank you.

Jason


ANSWER: Hi Jason,
Simply put, the revenue function is the demand function multiplied by quantity.
R(x) = x.p(x)

Regards

---------- FOLLOW-UP ----------

QUESTION: Thank you for responding. Really? x is quantity and Revenue R(x) is     xp(x)?
Someone told me Revenue R(x) is Cost times demand, or C(x)p(x).

http://answers.yahoo.com/question/index;_ylt=AroEFso6h7w5RxWqRgZznXHty6IX;_ylv=3

I solved the equation as such:

http://answers.yahoo.com/question/index;_ylt=AqBFCTK6wD1MnJcwTyfEe60AAAAA;_ylv=3

I'm not being cynical or condescending, I was just going by what I was told.


What's the difference between x and p(x)? Is x is quantity and p(x) is demand? What is demand measured in? Does that mean for every number of x units made, the demand will be p(x) units?

Please let me know-that's confusing.

Thank you.

Jason


Answer
Hi Jason,
Lets try to clear this up.
Usually, a demand function expresses demand (quantity) as a function of price. But of course it can also be the other way round, like we have in this situation where price is expressed as a function of quantity.
So, p(x) is not the number of units made but the price at which each unit can be sold. It therefore makes sense that R(x) = x.p(x)
C(x) is the total cost of producing x units (clearly not a selling price because that is what revenue is). Its not even the cost per unit price, so why would you multiply it by unit price? In saying that R(x) = C(x).p(x) you're multiplying two PRICES which is clearly wrong.
In the statement "Revenue is equal to the cost of the product times the number of quantities sold" in the link you provided, cost price is obviously being confused with selling price.

You can always get back to me.

Regards