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Your firm faces the following demand curve:  Q(P)=4,251,528/P^3.Your firm’s cost function is: TC(Q)=27Q

A Calculate the price elasticity of demand (as a function of price)    

B Calculate the profit function  

C Calculate the profit-maximizing quantity Q*

D Calculate the profit-maximizing price P*

E Calculate profits at the profit-maximizing price and quantity  

F Calculate the markup on price at the profit-maximizing price Note: Markup on Price=(P-MC)/P 

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Related questions

The demand function is Q = 100 - .5P. The cost function is TC = C = 100 + 60(Q) + (Q) 2

a. Find MR and MC

b. Demonstrate that profit is maximized at the quantity where MR = MC.

c. Derive the relationship between marginal revenue and the price elasticity of demand and show that the profit-maximizing price and quantity will never be the unit-elastic point on the demand curve.

d. Using the information in (b), demonstrate that the profit-maximizing price and quantity will never be in the inelastic portion of the demand curve.

2. A price-taking firm has a short run cost function SC(q)=3q^{2}+18q+600

a) In Problem #1, we showed that every q<7 would never be the profit-maximizing quantity at any price. Calculate SAVC(q) and MC(q) and use them to explain why for every q>0, there is a P for which that q is the profit-maximizing quantity.

b) Calculate the profit for this firm if the price is P = 72. Using either an integral or geometry, calculate the producer surplus for the firm at P = 72. Explain how the Producer surplus is related to the profit number.

c) Calculate P= p (72)- p (18). Explain how this number is related to the producer surplus.

 (18 points) Demand Estimation and Profit Maximization.

 Firm A usually charges $200 for its product and sells 1530 units per week.  In a market experiment it raises it price to $215 and sells 1020 units per week.  

1. (3 points)  Assuming that firm A’s demand function is linear (i.e., Q(P)=a-bP), estimate its demand function.    

2. (3 points) Firm A has fixed costs of $16,634 per week and variable costs of $147 per unit.  What is its cost function?  

3. (3 points)  What is firm A’s profit function?  

4. (3 points)  Calculate the profit maximizing quantity, Q^*, that firm A should produce  

5. (3 points)  Calculate the profit maximizing price that firm A should charge

  6. (3 points) Calculate profits at the profit maximizing price

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