Question

12. (Perfect Competition) The demand for a media art is given by Q=1,500-80p The long-run total costs for each firm is composed of wages for media artists and other operation costs. Each firm hires only one media artist regardless of output -25 1 a function of output, given by levels. Other operation costs are Q. 4 25 Q+ w,where w denotes the 4 Therefore, the long-run total cost is m+-0-0 wage for a media artist. The supply curve of media artists is L= (2w)/2, If both markets (media arts and media artists markets) are perfectly competitive, find long-run equilibrium output, price, and each firm's output Also, find long-run equilibrium wage and number of media artists in this media art market.

Answer 1

Under long run-equilibrium

For profit maximization condition. The LAC=LMC (Long run Average cost=Marginal cost)

1/2Q-25/4+w/Q=Q-25/4,we get w/Q=Q/2

Q²=2w

Also for perfectly competitive conditions,LMC=P(that is Marginal cost=Marginal revenue by producing one more output)

Q-25/4=P

Q=1500-80(Q-25/4)

79Q=1500+500

Q=25.316 rounding it to 25

and w=312.5

inserting this W into L=(2w)^1/2 we get L=25

and so long run equilibrium output Q= 25,price=Q-25/4=18.75

each firm's output=25/L (since each firm only hires one media artist)=1

Long run equilibrium wage=312.5 and number of media artists L= 25

Hope it helps