Answer to Question #221142 in Macroeconomics for Ja rule

Question

If the supply and demand function are given p=20e^0.4Q and p=100e^-0.2Q, respectively .find the equilibrium price and quantity ,and calculate the consumers and producers surplus

Answer 1

$At equilibrium, quantity supplied=quantity demanded$

Qd=p=100e^-0.2Q,

Qs=p=20e^0.4Q

change the exponential functions into linear functions

quantity supplied = ln P=0.4Q+ln 20

quantity demanded =ln P=-O.2Q+ln 100

0.4Q+20=0.2Q+100

0.2Q=80

Q=400

P=0.4Q+20

=28

Price=28

Quantity=400