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April 4th, 2017, 02:29 AM  #1 
Member Joined: Mar 2017 From: Israel Posts: 70 Thanks: 2  Microeconomics
Hello Can you help me please about the following exercise : Q=Amount Manufacturer produces a product. In front of him is a marginal cost function MC(Q)=Q and a demand function P=102*Q. What is the amount that maximizes the manufacturer's profits? a. 2 b. 10/3 c. 3 d. 13/4 e. 1 Thanks a lot! 
April 4th, 2017, 11:11 AM  #2 
Senior Member Joined: May 2016 From: USA Posts: 1,148 Thanks: 479 
Profit is maximized where marginal cost = marginal revenue. Do you see why? You are given the marginal cost function? What do you think the marginal revenue function is? 
April 4th, 2017, 12:04 PM  #3 
Member Joined: Mar 2017 From: Israel Posts: 70 Thanks: 2  
April 4th, 2017, 12:57 PM  #4 
Senior Member Joined: May 2016 From: USA Posts: 1,148 Thanks: 479 
The correct answer is NOT e. It is hard to guide you through this without knowing anything about what you know. Do you know differential calculus? Let's start at the beginning. Here is our simple model. $units\ sold = Q.$ $price\ per\ unit\ sold = P.$ $revenue = r = R(P,\ Q) = what?$ $cost = c = C(Q).$ $profit = r  c.$ Any questions about that model? Our economic assumption is that the owner wants to maximize profits. Last edited by JeffM1; April 4th, 2017 at 12:59 PM. 
April 4th, 2017, 11:23 PM  #5  
Member Joined: Mar 2017 From: Israel Posts: 70 Thanks: 2  Quote:
No questions, i understood Last edited by IlanSherer; April 4th, 2017 at 11:26 PM.  
April 5th, 2017, 05:30 AM  #6 
Senior Member Joined: May 2016 From: USA Posts: 1,148 Thanks: 479 
OK then. We maximize the profit function by taking its derivative and setting it equal to zero (ignoring the second derivative for now.) That is, profit is maximized when $R'  C' = 0 \implies R' = C'.$ The economists express that by saying profit is maximized where marginal revenue equals marginal cost. (This little formula ignores the second derivative issue.) Now in this particular problem, you are given the marginal cost curve as $C'(Q) = M(Q) = Q.$ Still with me? And obviously the derivative can only be taken with respect to Q. We are left with two issues. One is that the marginal revenue function cannot be found until we have found the revenue function itself. But the revenue function is simply unit price times units sold. So $R(P,\ Q) = PQ.$ Our second issue is that the revenue function depends on two variables. But marginal cost is expressed in terms of only Q. To equate derivatives, we need to reduce the revenue function to a function in Q. Do you see now how to finish up? 

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