Answer :
If demand is P = 20 - Qp and supply is P = 2 + 2Qs then the producer surplus in this scenario is 8.
The producer surplus in this scenario can be calculated by determining the area between the supply curve and the market price. In the given equations, the demand curve is represented by P = 20 - Qp, where P is the price and Qp is the quantity demanded, while the supply curve is represented by P = 2 + 2Qs, where Qs is the quantity supplied.
To find the equilibrium price and quantity, we set the demand and supply equations equal to each other:
20 - Qp = 2 + 2Qs
Simplifying the equation, we get:
Qp + 2Qs = 18
Now, we can solve for Qp in terms of Qs:
Qp = 18 - 2Qs
Substituting this into the demand equation, we have:
P = 20 - (18 - 2Qs)
P = 2Qs + 2
Thus, the equilibrium price is 2, and the equilibrium quantity is 8.
To calculate the producer surplus, we need to determine the area between the supply curve and the equilibrium price. Since the supply curve is linear, we can find the area of a triangle.
The base of the triangle is the difference between the equilibrium quantity and the quantity at which the supply curve intersects the price axis. Therefore, the base is 8 - 0 = 8.
The height of the triangle is the difference between the equilibrium price and the price at which the supply curve intersects the quantity axis. Hence, the height is 2 - 0 = 2.
The area of the triangle, and consequently the producer surplus, is given by:
(1/2) × base × height = (1/2) × 8 × 2 = 8
Therefore, the producer surplus in this scenario is 8.
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