Hi kennwatson!!
Since you are asking for a homework help and it is against the
policies of Google Answers to make your homework, I will not show the
complete solution to you. I will give you the main directives and
necessary concepts to help you to solve it, plus the answer figures
for checking purposes. I am pretty sure that your problem here is
related with some missing concepts, so I think that this answer will
be helpful to you.
As a reference you can see the answer given by me to a related question:
"Google Answers: marginal analysis and economics":
http://answers.google.com/answers/threadview?id=566631
First of all the function D(x) is an inverse demand function, a demand
function gives quantity demanded (x) as a function of price of good
(P). The inverse demand function is just the inverse of the demand
function that is a new function that gives the price of a good (P) as
a function of the quantity demanded (x); this is what you have in the
statement of the problem. So D(x) gives us the correspondent price for
the quantity 'x' demanded for the market.
Now the problem:
1. write the revenue function.
Revenue = quantity demanded * unit price =
= x * D(x) =
etc.
Answer: -70*x^2 + 870*x
2. write the (total) cost function.
C(x) = Variable costs + fixed costs =
= quantity demanded * variable cost per unit + 0 =
etc.
Answer: 590*x
3. write the profit function.
This one is easy:
Profit = Revenue - Cost
So just subtract cost function from the revenue function.
Answer: -70*x^2 + 280*x
4. what is the marginal cost when x=4
This is the hardest point, you must calculate a derivative, but in
this case is an easy one!!
Marginal Profit is the additional profit derived from the sale of one
additional unit, and it is easy calculated as the derivative of the
profit.
You will find nice references at the answer of the "Google Answers:
marginal analysis and economics" question.
Marginal Profit = Derivative of Profit =
= (-70*x^2 + 280*x)'
etc.
Here the answer is the next step, so I will not show it to you yet,
please just do it yourself and if you need to check it I will confirm
you the figure if you post what you have found.
I hope that this helps you. Feel free to use the clarification feature
to request for further assistance on this question if you need it.
Best regards,
livioflores-ga |
Request for Answer Clarification by
kennwatson-ga
on
11 Oct 2005 09:23 PDT
so would the marginal cost be 590 or 590(4)=2360
|
Request for Answer Clarification by
kennwatson-ga
on
11 Oct 2005 09:37 PDT
sorry i think it might be now-
-140(4)+280=280
|
Clarification of Answer by
livioflores-ga
on
11 Oct 2005 10:20 PDT
Hi again!!
Your last answer is very close to be right, please check the result,
you are right with (-70*x^2 + 280*x)' = -140*x + 280, but the result
is incorrect.
|
Request for Answer Clarification by
kennwatson-ga
on
11 Oct 2005 16:07 PDT
is it -280 and if it is can that happen.
|
Clarification of Answer by
livioflores-ga
on
11 Oct 2005 16:34 PDT
Yes, surprisingly the marginal profit is negative, this means that the
additional profit is actually an additional loss, in other words,
profit decreases if you increase the output due the high cost per unit
related to its price.
Note that the price at 4 units demanded is 590 each unit, an the cost
to produce the 4 units is 590*4, so you have no profit at this point.
At 3 units demanded you have a price of 660 each unit, then the
revenue is 1980 and a total cost of 1770, and the profit is 210.
Producing one more unit to satisfy a demand of four units the profit
decreases from 210 to zero, this is why the marginal profit at 4 is
negative.
Regards,
livioflores-ga
|
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