Question

Suppose the supply is given by P=2+Q, and the equilibrium price is $6. What is the value of the producer surplus?

Answer 1

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.