Suppose that the demand for x units of some product is p =
20,000-150x, and the cost of producing x units is given by C(x) =
8000+1.2x^2-22x. Find the marginal profit from the produciton of 86
units

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Request for Question Clarification by livioflores-ga on 08 Oct 2005 15:04 PDT

Hi!!

The demand is the quantity of products needed to satisfied a
competitive  market requirements. This is a function of the price (P),
so you can say that demand (Q) is:
Q = f(P), that defines Q in function of P, and you can find the
inverse demand function (needed to calculate revenues at a given
price) as the inverse function for the demand, then is:
P = f^-1(Q) , that defines P in function of Q.

I think that you have misstated this problem, could be the named p(x)
function be the inverse demand function, that is the function that
defines the price in function of the demand (named x by you)?
 
Thank you.

The demand function is fine. You should specify wehat kind of market
we are talking about. Are you talking about a monopoly and ask what is
its marginal profit, or about perfect competition?