Question

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.
$p = d(x)=80e^{-0.004x}$; $p = s(x)=35e^{0.004x}$
the value of x at equilibrium is 103
(round to the nearest whole number as needed.)
the value of p at equilibrium is $□$
(round to the nearest dollar as needed.)

Explanation:

Step1: Substitute \(x = 103\) into the price - supply equation

We know the price - supply equation \(p=S(x)=35e^{0.004x}\).
Substitute \(x = 103\) into it: \(p = 35e^{0.004\times103}\).
First, calculate the exponent: \(0.004\times103=0.412\).
Then, \(e^{0.412}\approx1.509\).
So, \(p = 35\times1.509\).

Step2: Calculate the value of \(p\)

\(p=35\times1.509 = 52.815\approx53\).

Answer:

\(53\)