Answer to Question #221283 in Microeconomics for Emma

Question

If the supply and demand functions are given by 20e^0.4Q and P = 100e^-0.2Q respectively, find the equilibrium price and quantity, and calculate the consumer’s and producer’s surplus

Answer 1

Equating SUPPLY=DEMAND

Supply

$0.4Q=ln\frac{P}{20}$

$Q=\frac {ln\frac {P}{20}}{0.4}$ …supply

$-0.2Q=ln\frac{P}{100}$

$Q=\frac{-ln\frac{P}{100}}{0.2}$ …demand

$\frac {lnP-ln20}{0.4}=\frac {-lnP+ln100}{0.2}$

$P=96.15$

Substituting P in the equation for supply:

we get $Q=4.$

Equilibrium price=96.15

Equilibrium quantity= 4