Solve the problem.
-Suppose the demand function of a certain item is given by $D(x)=2 e^{x}$ and the supply function is $S(x)=8 e^{-x}$. Find the consumer's surplus. Round to three decimal places.
A) 1.227
B) 0.773
C) 1.337
D) 0.664

Question

Quizplus · Accepted Answer

The consumer's surplus is calculated by finding the area between the demand curve and the equilibrium price level up to the equilibrium quantity. First, find the equilibrium by setting $D(x) = S(x)$: $2e^x = 8e^{-x}$. Solving gives $x = \ln(2)$. The equilibrium price is $D(\ln(2)) = 4$. The consumer's surplus is $\int_0^{\ln(2)} (2e^x - 4) \, dx$, which evaluates to approximately 1.227.

Solve the Problem D(x)=2exD(x)=2 e^{x}D(x)=2ex And the Supply Function Is S(x)=8e−xS(x)=8 e^{-x}S(x)=8e−x

Solve the Problem $D(x)=2 e^{x}$ And the Supply Function Is $S(x)=8 e^{-x}$