what is the consumer surplus, producer surplus and deadweight loss if a monopolist has demand p=100-Q and Cost= 10Q
Thanks xox
I presume you can determine the price the monopolist will charge. (hint: MR=100-2Q, MC=10)
Draw a graph showing the demand line, the MC line, the MR line, the maximizing price and quantity.
Consumer surplus will be the triangle area below demand but above price. Producer surplus will be the rectangle area below price but above MC, and to the left of Q. Deadweight loss will be the triangle area below the demand curve, above the MC line, and to the right of Q.
To find the consumer surplus, producer surplus, and deadweight loss in this scenario, we need to understand the concepts and calculate them step by step.
Consumer Surplus:
Consumer surplus represents the difference between what consumers are willing to pay for a good or service and what they actually pay. It measures consumer satisfaction and benefit from a transaction. We can calculate it by finding the area under the demand curve and above the market price.
In this case, the market price equals the monopolist's price, which is given as P = 100 - Q. To find the consumer surplus, we need to determine the quantity demanded at this price. By substituting the price equation into the demand equation, we get:
P = 100 - Q
100 - Q = 100 - Q
Q = 0
Therefore, at a price of 100, the quantity demanded is 0. The consumer surplus is calculated as the area of the triangle formed by the price (100) and the y-axis (0) and the quantity (0) and the x-axis (0). Since it is a triangle, the area can be calculated using the formula:
Consumer Surplus = (1/2) * (Base) * (Height)
Consumer Surplus = (1/2) * (100 - 0) * (0 - 0)
Consumer Surplus = 0
Producer Surplus:
Producer surplus represents the difference between what producers receive for selling a good or service and the minimum price at which they are willing to sell it. It measures producer benefit and profit. To calculate producer surplus, we need to find the area below the market price and above the supply curve.
In this case, the monopolist's price is P = 100 - Q. To calculate the producer surplus, we need to determine the quantity supplied at this price. The quantity supplied can be found by substituting the price equation into the supply equation, which is given as:
P = MC (Marginal Cost) = 10Q
100 - Q = 10Q
100 = 11Q
Q = 100/11
Therefore, at a price of 100, the quantity supplied is 100/11. The producer surplus is calculated as the area of the triangle formed by the price (100) and the y-axis (100/11) and the quantity (100/11) and the x-axis (0). Using the triangle area formula mentioned before:
Producer Surplus = (1/2) * (Base) * (Height)
Producer Surplus = (1/2) * (100 - 0) * (100/11 - 0)
Producer Surplus = 5000/11
Deadweight Loss:
Deadweight loss represents the efficiency loss caused by a market distortion, which in this case is a monopoly. It occurs when the quantity produced by a monopolist is lower than the quantity produced in a perfectly competitive market. Deadweight loss is measured by the area of the triangle between the supply curve and the demand curve, which is not being transacted in the monopoly scenario.
To calculate the deadweight loss, we need to find the difference between the quantity produced by the monopolist (Q = 100/11) and the quantity that would have been produced in a perfectly competitive market (Q = 100).
Deadweight Loss = (1/2) * (Base) * (Height)
Deadweight Loss = (1/2) * (100 - 100/11) * (100/11 - 100)
Deadweight Loss = 90000/121
Thus, in this scenario, the consumer surplus is 0, the producer surplus is 5000/11, and the deadweight loss is 90000/121.