Question

Pd=20e^0.4Q and Ps=100e^-0.4Q find the equilibrium price and quantity

Answer 1

According to microeconomics at equilibrium

$Ps = Pd$

$20e^{0.4Q}= 100e^{-0.4Q}$

$20e^{0.8Q}= 100$

$e^{0.8Q} = \frac{100}{20}$

$0.8Q = ln 5$

$Q= \frac{5}{4} ln 5$

Use the value of Q in the equation

$20^{0.4(5/4 ln5)}$

$20^{0.5 ln 5}$

Equilibrium price = $20e^{0.5ln 5}$

Quantity= $\frac{5}{4} ln 5$