A monopoly can produce any level of output it wishes at a constant marginal (and average) cost of $5 per unit. Assume the monopoly sells its goods in two different markets separated by some distance. The demand curve in the first market is given by Q1 = 55 - P1, and the demand curve in the second market is given by Q 2 = 70 - 2P2
i. If the monopolist can maintain the separation between the two markets, what level of output should be produced in each market, and what price will prevail in each market?
If the monopoly powers broke and the monopolist is constrained to behave like a perfectly competitive firm, how would the answers in part i above change? What is the value of dead weight loss in the two markets due to monopoly existence?
a monopoly face demand schedule p=230-q and the demand function and the cost schedule TC=10+0.25q2 then determine the elasticity of demand of maximum revenues ?
To determine the level of output and price in each market, we need to find the profit-maximizing level of output in each market for the monopolist.
i. The profit-maximizing condition for a monopolist is Marginal Revenue (MR) = Marginal Cost (MC).
In the first market, the demand curve is given by Q1 = 55 - P1. To find the Marginal Revenue, we differentiate this equation with respect to Q1.
dQ1/dP1 = -1
To find Marginal Revenue, we multiply the derivative by (-1) and equate it to MC.
MR1 = MC = $5
Now, set MR1 equal to its demand function to solve for P1:
55 - P1 = 5
P1 = 50
Substituting this value of P1 back into the demand equation Q1 = 55 - P1:
Q1 = 55 - 50
Q1 = 5
Therefore, the monopolist should produce 5 units of output and set the price at $50 in the first market.
Similarly, for the second market, the demand curve is given by Q2 = 70 - 2P2. Following the same steps as above:
dQ2/dP2 = -2
MR2 = MC = $5
Set MR2 equal to its demand function to solve for P2:
70 - 2P2 = 5
2P2 = 70 - 5
2P2 = 65
P2 = 32.5
Substituting this value of P2 back into the demand equation Q2 = 70 - 2P2:
Q2 = 70 - 2(32.5)
Q2 = 70 - 65
Q2 = 5
Therefore, the monopolist should produce 5 units of output and set the price at $32.5 in the second market.
ii. If the monopoly power is broken, and the monopolist behaves like a perfectly competitive firm, the level of output and price in each market will change. In a perfectly competitive market, individual firms are price takers and cannot influence the market price.
In a perfectly competitive firm, the firm's output level is determined by the intersection of the market supply curve and the market demand curve. However, since the separation between the two markets is maintained, they would still act as separate markets.
The market price in each market will be determined by the intersection of the market supply and demand curves. Without further information about the supply curves in the markets, we cannot determine the new prices and output levels.
The deadweight loss is the measure of efficiency loss due to the existence of a monopoly. It represents the decrease in total surplus that occurs when compared to a perfectly competitive market. To calculate the deadweight loss, we would need the total surplus values resulting from the perfect competition scenario and then compare it to the monopoly scenario by calculating the difference. Unfortunately, without specific numerical values, we are unable to determine the exact value of the deadweight loss in each market.