Solve the problem.
-Find the producer's surplus if the supply function of some item is given by $S(x)=x^{2}+2 x+8$. Assume that supply and demand are in equilibrium at $x=30$.
A) 17,200
B) 12,700
C) 18,900
D) 19,800

Question

Quizplus · Accepted Answer

The producer's surplus is calculated by finding the area between the supply curve and the equilibrium price line from 0 to the equilibrium quantity. First, find the equilibrium price by substituting $x=30$ into the supply function: $S(30) = 30^2 + 2(30) + 8 = 968$. The producer's surplus is the integral of the supply function from 0 to 30 minus the equilibrium price times the equilibrium quantity: $\int_0^{30} (x^2 + 2x + 8) \, dx - 968 \times 30 = 18,900$.

Solve the Problem S(x)=x2+2x+8S(x)=x^{2}+2 x+8S(x)=x2+2x+8 Assume That Supply and Demand Are in Equilibrium At Function

Solve the Problem $S(x)=x^{2}+2 x+8$ Assume That Supply and Demand Are in Equilibrium At Function