Question

Suppose demand and supply are given by

Q_X^d = 14 - (1/2)P_X  and Q_X^s= (1/4)P_X - 1

Instructions: Enter your responses rounded to the nearest whole number.

a. Determine the equilibrium price and quantity. Show the equilibrium graphically.

Equilibrium price: $

Equilibrium quantity:

Instruction: Use the tools provided to graph the inverse supply function 'S' and the inverse demand function 'D' from X = 0 to X = 6 (two points total for each) and indicate the equilibrium point.

b. Suppose a $12 excise tax is imposed on the good. Determine the new equilibrium price and quantity.

Equilibrium price: $

Equilibrium quantity:

c. How much tax revenue does the government earn with the $12 tax?

$

Please show hand written step by step work to understand calculations

Answer 1

Demand and supply are given by Q_X^d = 14 - (1/2)P_X  and Q_X^s= (1/4)P_X - 1

a. Find equilibrium price using Qd = Qs

14 - P/2 = P/4 - 1

15 = 3P/4

P = 20 and Q = 4 units

Equilibrium price: $20 per unit

Equilibrium quantity: 4 units

b. Now a $12 excise tax is imposed on the good. New supply equation is Qx = (1/4)(P - 12) - 1

New equilibrium has

Qd = Qs

14 - P/2 = P/4 - 12/4 - 1

18 = 3P/4

P = 24 (paid buy buyers)

Q = 14 - 24/2 = 2 units

P = 24 - tax = 24 - 12 = 12 (received by sellers)

Equilibrium price: $24

Equilibrium quantity: 2 units

c. Tax revenue = tax rate * quantity sold = $12 * 2 = $24.