Suppose the supply is given by P=2+Q, and the equilibrium price is $6. What is the value of the producer surplus?
To find the value of the producer surplus, we need to calculate the area between the equilibrium price ($6) and the supply curve (P = 2 + Q), up to the quantity where the price equals the equilibrium price.
The equilibrium price is given as $6. Substituting this value into the supply equation gives:
6 = 2 + Q
Subtracting 2 from both sides, we find:
Q = 6 - 2
Q = 4
So, at the equilibrium price of $6, the quantity supplied is 4.
To calculate the producer surplus, we need to find the area between the supply curve and the price line (P = $6), up to the quantity of 4.
The supply curve is given as P = 2 + Q. Substituting the quantity of 4 into this equation, we find:
P = 2 + 4
P = 6
Since this price (P = $6) is equal to the equilibrium price, it forms the upper bound of the area we are interested in.
To find the area between the supply curve and the price line, we need to calculate the difference between the price line and the supply curve (P - (2 + Q)) and multiply it by the quantity (4).
P - (2 + Q) = 6 - (2 + 4)
P - (2 + Q) = 6 - 6
P - (2 + Q) = 0
The difference between the price line and the supply curve (P - (2 + Q)) is 0. And multiplying this difference by the quantity gives us:
0 * 4 = 0
Therefore, the value of the producer surplus is $0.
To find the value of producer surplus, we need to calculate the area between the supply curve and the equilibrium price.
Step 1: Find the equilibrium quantity.
Given that the equilibrium price is $6, we can substitute this value into the supply equation to find the equilibrium quantity.
P = 2 + Q
$6 = 2 + Q
Q = $6 - $2
Q = 4
Step 2: Calculate the area of the producer surplus.
To calculate the producer surplus, we need to find the difference between the equilibrium price and the marginal cost for each unit produced, and sum them up.
Since the supply curve is given by P = 2 + Q, we can substitute the equilibrium quantity (Q = 4) to find the marginal cost (MC) at this level.
MC = 2 + Q
MC = 2 + 4
MC = $6
Now we can calculate the producer surplus.
Step 3: Calculate the area of the producer surplus (PS).
We need to find the area between the supply curve (MC) and the equilibrium price ($6) up to the equilibrium quantity (Q = 4).
The formula to calculate the area of a triangle is: (base * height) / 2.
Base: The base of the triangle is the quantity (Q = 4).
Height: The height of the triangle is the difference between the equilibrium price ($6) and the marginal cost (MC = $6).
PS = (Q * (P - MC)) / 2
PS = (4 * ($6 - $6)) / 2
PS = (4 * $0) / 2
PS = $0
Therefore, the value of the producer surplus is $0.
To find the value of the producer surplus, we need to first determine the equilibrium quantity.
Since supply is given by P=2+Q, where P represents the price and Q represents the quantity supplied, we can rearrange the equation to solve for Q:
P = 2 + Q
Q = P - 2
We know that the equilibrium price is $6, so we substitute P = 6 into the equation to find the equilibrium quantity:
Q = 6 - 2
Q = 4
Now that we know the equilibrium quantity is 4, we can find the value of the producer surplus.
Producer surplus represents the difference between what producers are willing to accept for a product and what they actually receive at the equilibrium price. In this case, the producers are willing to accept a minimum of their marginal cost, which is the price at which they are willing to supply the product.
To calculate the producer surplus, we first need to find the area between the supply curve and the equilibrium price.
The equation of the supply curve is P = 2 + Q, where P is the price and Q is the quantity supplied.
Plugging in the equilibrium price P = 6, we can solve for Q:
6 = 2 + Q
Q = 6 - 2
Q = 4
So, at the equilibrium price of $6, the equilibrium quantity is 4. We can plot this point on a graph.
Now, the producer surplus is the area between the supply curve and the equilibrium price ($6) from 0 to the equilibrium quantity (4).
To calculate the producer surplus, we need to calculate the area of the triangle formed by the supply curve, the x-axis (quantity), and the equilibrium quantity.
The formula to calculate the area of a triangle is:
Area = 1/2 * base * height
The base of the triangle is the equilibrium quantity, which is 4.
The height of the triangle is the difference between the equilibrium price and the price at which the supply curve intersects the x-axis (quantity).
The price at which the supply curve intersects the x-axis can be found by setting P = 0 in the supply equation:
0 = 2 + Q
Q = -2
Therefore, the height is the difference between the equilibrium price ($6) and the price at which the supply curve intersects the x-axis, which is also $6.
Height = 6 - 0 = 6
Now, we can calculate the producer surplus:
Producer Surplus = 1/2 * base * height
Producer Surplus = 1/2 * 4 * 6
Producer Surplus = 12
Therefore, the value of the producer surplus is $12.