Answer to Question #93498 in Microeconomics for Musbahu Ibrahim Ahmad

Question

A firm face inverse demand curve p=150-0.25Q with total cost function TC=2000+22.5Q
Assuming the firm maximizes profits Answer the following:
1* firm operates as a monopolist calculate the (a) price (b)quantity (c)profit show the graph of equilibrium price and quantity
2*Assuming perfect competition calculate the (a)price (b)quantity (c)profit.show the equilibrium price and quantity

Answer 1

1* firm operates as a monopolist 

MR = MC

MR = TR' = (P*Q)' = ((150-0.25Q)*Q)' = 150 - 0.5*Q

MC = (TC)' = (2000+22.5Q )' = 22.5

150 - 0.5*Q = 22.5

- 0.5*Q = -127.5

Q = 255 - equilibrium quantity

P = 150 - 0.25*255 = 86.25 - equilibrium price

profit = 255*86.25 = 21993.75

2*Assuming perfect competition

MR = MC, MR = P

P = MC

MC = (TC)' = (2000+22.5Q )' = 22.5

150-0.25Q = 22.5

-0.25Q = -127.5

Q = 510 - equilibrium quantity

p=150-0.25Q = 150 - 0.25*510 = 22.5 - equilibrium price

profit = 22.5*510 = 11475