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 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: 6,494 Thanks: 577 What is Q?
 March 24th, 2018, 03:14 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,089 Thanks: 846 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: 18,838 Thanks: 1564 When solving for Q, choose the positive solution.

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