The producer surplus for the demand and supply functions x+y=4 and -x+y=2 is?
To find the producer surplus for the given demand and supply functions, we first need to determine the equilibrium price and quantity.
The demand and supply are represented by the equations:
Demand: x + y = 4
Supply: -x + y = 2
To find the equilibrium, we set the demand equal to the supply:
x + y = -x + y
Rearranging this equation, we get:
2x = 2
Dividing both sides by 2, we find:
x = 1
Now we can substitute this value of x into either the demand or supply equation to find the equilibrium quantity. Let's use the supply equation:
-x + y = 2
Substituting x = 1, we have:
-1 + y = 2
Adding 1 to both sides gives us:
y = 3
So, the equilibrium price is x = 1 and the equilibrium quantity is y = 3.
The producer surplus is the area above the supply curve and below the equilibrium price. To calculate it, we need to find the area of the triangle formed by the supply curve and the equilibrium quantity.
First, we need to find the price at the equilibrium point. Substituting x = 1 and y = 3 into the supply equation, we get:
-1 + 3 = 2
So, the equilibrium price is 2.
Next, we calculate the base and height of the triangle:
Base = Quantity = 3
Height = Price = 2
Now we can use the formula for the area of a triangle:
Area = (base * height) / 2
Substituting in the values, we have:
Area = (3 * 2) / 2 = 3
Therefore, the producer surplus for the given demand and supply functions is 3.