Answer to Question #289210 in Microeconomics for Fazi

Question

Suppose market of a good x can be illustrated by following two equations.

Deman P= 82-0.07Q

Supply P= 14+0.09Q

a) Calculate the equilibrium and quantity in the market.

b) Suppose a tax of $3 is imposed on the supplier of this market. Calculate the quantity after tax, consumer's price, producer's price and government revenue.

Answer 1

Solution:

a.). At equilibrium: Qd = Qs

82 – 0.07Q = 14 + 0.09Q

82 – 14 = 0.09Q + 0.07Q

68 = 0.16Q

Q = 425

Equilibrium quantity = 425

Substitute to derive equilibrium price:

P = 82 – 0.07Q

P = 82 – 0.07(425) = 82 – 29.75 = 52.25

P = 52.25

Equilibrium price = 52.25

 

b.). New supply curve after tax: P = 17 + 0.09Q

New equilibrium: Qd = Qs

82 – 0.07Q = 17 + 0.09Q

82 – 17 = 0.09Q + 0.07Q

65 = 0.16Q

Q = 406.25

Quantity after tax = 406.25

P = 82 – 0.07(406.25) = 82 – 28.44 = 53.56

P = 53.56

Consumer price = 53.56

Producer price = 14 + 0.09(406.25) = 14 + 36.56 = 50.56

Government revenue = 3 $\times$ 406.25 = 1,218.75