March 21st, 2018, 11:27 AM  #1 
Newbie Joined: Mar 2018 From: Wales Posts: 1 Thanks: 0  Help pls!
The demand and total cost functions for a monopolist are given as Demand function: P = 210 – 5Q; Total cost function: TC = Q^3– 2Q^2 + 15Q + 60 (a) Derive the total revenue function and calculate the level of output to give maximum total revenue. (b) Derive the profit function and calculate the level of output to give maximum profit (or minimum loss). (c) Calculate the price elasticity of demand as output with the maximum profit (or minimum loss) level. 
March 21st, 2018, 12:18 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,540 Thanks: 591 
What is Q?

March 24th, 2018, 03:14 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,244 Thanks: 887 
Assuming "standard practice", "P" is the price at which a commodity is offered and "Q" is the quantity purchased at that price. Given that the demand function is P= 210 5Q then the revenue is that price multiplied by the quantity sold, QP= 210Q 5Q^2. To find the maximum of that either set the derivative equal to 0 or, since this is a quadratic, complete the square. The cost of production is given by Q^3 2Q^2+ 150Q+ 60. The profit is revenue minus cost: 210Q 5Q^2 (Q^3 2Q^2+ 150Q+ 60)= Q^3 3Q^2+ 60Q 60. To find the maximum profit set the derivative of that equal to 0 and solve for Q. 
March 24th, 2018, 04:48 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 19,178 Thanks: 1646 
When solving for Q, choose the positive solution.


Tags 
demand, monopolist, pls, price elasticity, total cost, total revenue 
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