Applied Maxima and Minima Problem

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SUMMARY

The discussion focuses on solving an applied maxima and minima problem related to a monopolist's product, specifically using the demand equation p=156-2q and the average cost function c(ave)=120+112/q. The user seeks assistance in deriving the total cost function from the average cost and calculating the net profit, which is expressed as 112 + 36q - 2q². The solution involves completing the square to find the maximum profit value.

PREREQUISITES
  • Understanding of demand equations in economics
  • Knowledge of average cost functions
  • Familiarity with profit maximization techniques
  • Ability to complete the square in algebra
NEXT STEPS
  • Study the derivation of total cost functions from average cost functions
  • Learn about profit maximization in monopolistic markets
  • Explore the concept of completing the square in quadratic equations
  • Research the implications of demand elasticity on pricing strategies
USEFUL FOR

Economics students, business analysts, and anyone involved in pricing strategy and profit optimization in monopolistic markets.

jennifer361
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Homework Statement


Problem goes like this:
For a monopolist's product, the demand equation is: p=156-2q
_
and the average-cost is c(ave)=120+112/q


Homework Equations


We need to find the total cost function in terms of c=


The Attempt at a Solution



I can't seem to figure out how to change the average cost of cost...or maybe it's simple and I'm completely missing it...any help would be greatly appreciated!
 
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I'm going to assume that p is the "demand"- the number of items purchased- at price c. (In the future it would be helpful to say things like that explicetely.) Then the revenue is pq= (156-2q)q= 156q- 2q2. The average cost of each item 120- 112/q so the cost of q items is (120- 112/q)q= 120q- 112. (I have no idea what "average cost of cost" means!).

Finally, the net profit is the revenue minus the cost: 156q- 2q2- (120 q- 112)= 112+ 36q- 2q2. You should be able to find the maximum value of that by completing the square.
 

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