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 $x$ at equilibrium is $◻$ .

Answer

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Answer

Round the equilibrium quantity to the nearest integer: $154$

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: $154$