Problem

Find the consumers' surplus and the producers' surplus at the equilibrium price level for the given price-demand and price-supply equations. Include a graph that identifies the consumers' surplus and the producers' surplus. Round all values to the nearest integer.
\[
p=D(x)=140 e^{-0.005 x} ; p=S(x)=30 e^{0.005 x}
\]

The value of $\mathrm{x}$ at equilibrium is $\square$.

Answer

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Answer

Round the equilibrium quantity to the nearest integer: \(\boxed{154}\)

Steps

Step 1 :Set the demand equation equal to the supply equation: \(140 e^{-0.005 x} = 30 e^{0.005 x}\)

Step 2 :Solve the equation for x to find the equilibrium quantity.

Step 3 :The equilibrium quantity, x, is approximately 154.044504094715.

Step 4 :Round the equilibrium quantity to the nearest integer: \(\boxed{154}\)

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