Question

The market demand is described by the equation Q = 2020 - 2P and the total...

The market demand is described by the equation Q = 2020 - 2P and the total cost function for each firm is C(q) = 0.5q2 + 10q + 50. What is the long run price in this industry?

20

18

120

10

Business   Economics   
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Answer #1

Given Q = 2020 - 2P

C(Q) = 0.5Q2 + 10Q + 50

frpm the first equation we get

P= 1010 - 0.5Q

We know tha In the long run

Marginal revenue = Marginal Cost

Total revenue= price * quantity

  =P*Q

  =(1010-.5Q)*Q

  =1010Q-.5Q2

Marginal revenue= d(total revenue)/dQ

  =d(1010Q-.5Q2)/dQ

  = 1010-Q

Marginal Cost = d(total cost)/dQ

=d(0.5Q2 + 10Q + 50)/dQ

=Q+10

We know tha In the long run

Marginal revenue = Marginal Cost

1010 - Q = Q + 10

Q=500

substituting Q in P= 1010 - 0.5Q

we get P=760 ans

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