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corie corie
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7 years ago
A firm's demand curve is given by P = 500 - 2Q.  The firm's current price is $300 and the firm sells 100 units of output per week.

a.   Calculate the firm's marginal revenue at the current price and quantity using the expression for marginal revenue that utilizes the price elasticity of demand.
b.   Assuming that the firm's marginal cost is zero, is the firm maximizing profit?
Textbook 
Microeconomics

Microeconomics


Edition: 8th
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#1
7 years ago
a.       
Begin by calculating the price elasticity of demand, ED:
   ED =   ∙ 
To find   solve for Q in terms of P.
   P = 500 - 2Q
   P - 500 = -2Q
   Q = 250 - 0.5P

     = -0.5; ED =   ∙ 
     = -0.5 ∙   = -1.5
   MR = P + P ( )
   MR = 300 + 300 ( )
   MR = 300 - 200 = 100

b.       
If MC = 0, the firm is not maximizing profit since MR should be equal to MC.  The firm  should expand output.
   MR = 500 - 4Q = 0
   4Q = 500
   Q = 125
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