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March 21st, 2018, 11:27 AM   #1
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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

(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.
charleyemmett is offline  
March 21st, 2018, 12:18 PM   #2
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What is Q?
mathman is offline  
March 24th, 2018, 03:14 AM   #3
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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.
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March 24th, 2018, 04:48 AM   #4
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When solving for Q, choose the positive solution.
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