In a perfect competitive market, industry demand is P = 850 – 2Q, and industry supply is P = 250 + 4Q (supply is the sum of the marginal cost curves of the firms in the industry). Assume that all the firms collude to form a single monopoly firm. There is no change in the demand or cost conditions of the industry. What are the economic effects (price and quantity) of such a change in industry structure?
See my previous post on calculating the optimal quantity, then price. Compare that to the competitive case where supply=demand or 850-2Q=250+4Q -- solve for Q.
To determine the economic effects of the change in industry structure from perfect competition to a monopoly, we need to compare the equilibrium price and quantity in both scenarios.
1. Perfect Competition:
In a perfectly competitive market, the equilibrium price and quantity are determined at the intersection of industry demand and supply. Set the industry demand and supply equations equal to each other to find the equilibrium quantity:
850 - 2Q = 250 + 4Q
Simplifying this equation gives you:
6Q = 600
Q = 100
Substitute the value of Q back into either the demand or supply equation to find the equilibrium price:
P = 850 - 2(100)
P = 650
So, the equilibrium price in perfect competition is $650, and the equilibrium quantity is 100 units.
2. Monopoly:
In a monopoly, there is a single firm that has control over the market. The firm maximizes its profits by producing the quantity where marginal cost (MC) equals marginal revenue (MR). The monopolist's marginal cost is the same as the industry supply curve.
Set the industry supply equation equal to the marginal cost equation to find the monopolist's equilibrium quantity:
250 + 4Q = MC
Since MC is equal to supply in this case, we can conclude that MC = 250 + 4Q.
Now, set MR equal to the industry demand equation to find the monopolist's marginal revenue:
MR = 850 - 2Q
To maximize profits, the monopolist produces the quantity where MR = MC. Therefore, set 850 - 2Q equal to 250 + 4Q:
850 - 2Q = 250 + 4Q
Simplifying this equation gives you:
6Q = 600
Q = 100
So, the monopolist's equilibrium quantity is also 100 units.
Substitute the value of Q back into either the demand or supply equation to find the monopolist's equilibrium price:
P = 850 - 2(100)
P = 650
Therefore, the monopolist's equilibrium price is $650, which is the same as in perfect competition. However, the quantity produced under monopoly is lower than in perfect competition.