Suppose there are four firms in a competitive market and that each firm has the following supply function.
Supply functions for competitive firms
Company Supply Function
1 Q1 = 16 + 4P
2 Q2 = -5 + 5P
3 Q3 = 32 + 8P
4 Q4 = - 60 +10P
a. Find the competitive market supply function.
b. If the market demand function for this product is Q = 500 - 2P , what is the competitive market price and quantity.
To find the competitive market supply function, we need to sum up the individual supply functions of each firm.
a. Competitive market supply function:
To find the market supply function, we add up the quantities supplied by each firm at a given price.
Q_market = Q1 + Q2 + Q3 + Q4
Substituting the supply functions of each firm:
Q_market = (16 + 4P) + (-5 + 5P) + (32 + 8P) + (-60 + 10P)
Simplifying:
Q_market = 16 - 5 + 32 - 60 + 4P + 5P + 8P + 10P
Q_market = -17 + 27P
Therefore, the competitive market supply function is Q_market = -17 + 27P.
b. To find the market price and quantity, we need to solve for the equilibrium point where the market supply equals the market demand.
Setting the market supply equal to the market demand:
-17 + 27P = 500 - 2P
Simplifying:
29P = 517
Dividing both sides by 29:
P = 17.8276
Now, substitute this value of P back into the market demand function to find the quantity:
Q = 500 - 2P
Q = 500 - 2(17.8276)
Q = 500 - 35.6552
Q = 464.3448
Therefore, in the competitive market, the price will be approximately 17.83 and the quantity will be approximately 464.34.