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Suppose demand and supply are given by Q_x^d=7- 1/2 P_x and Q_x^s= 1/4 P_x- 1/2a.Determine the equilibrium price and quantity. Show the equilibrium graphically. b.Suppose a $6 excise tax is imposed on the good. Determine the new equilibrium price and quantity.c.How much tax revenue does the government earn with the $6 tax?

Question

Suppose demand and supply are given by Q_x^d=7- 1/2 P_x and Q_x^s= 1/4 P_x- 1/2a.Determine the equilibrium price and quantity. Show the equilibrium graphically. b.Suppose a 6excisetaxisimposedonthegood.Determinethenewequilibriumpriceandquantity.c.Howmuchtaxrevenuedoesthegovernmentearnwiththe6 excise tax is imposed on the good. Determine the new equilibrium price and quantity.c.How much tax revenue does the government earn with the 6 tax?

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Solution

a. To find the equilibrium price and quantity, we need to set the quantity demanded (Q_x^d) equal to the quantity supplied (Q_x^s) and solve for P_x (price).

So, 7 - 1/2 P_x = 1/4 P_x - 1/2

Solving for P_x, we get P_x = 8. This is the equilibrium price.

Substituting P_x = 8 into either the demand or supply equation will give us the equilibrium quantity. Let's use the demand equation:

Q_x^d = 7 - 1/2 * 8 = 7 - 4 = 3. So, the equilibrium quantity is 3.

b. If a $6 excise tax is imposed on the good, the supply equation becomes Q_x^s = 1/4 (P_x - 6) - 1/2. Setting this equal to the demand equation and solving for P_x gives us the new equilibrium price.

7 - 1/2 P_x = 1/4 (P_x - 6) - 1/2

Solving for P_x, we get P_x = 10.4. This is the new equilibrium price.

Substituting P_x = 10.4 into either the demand or supply equation will give us the new equilibrium quantity. Let's use the demand equation:

Q_x^d = 7 - 1/2 * 10.4 = 7 - 5.2 = 1.8. So, the new equilibrium quantity is 1.8.

c. The tax revenue that the government earns with the 6taxisthetaxperunittimesthequantitysold,whichis6 tax is the tax per unit times the quantity sold, which is 6 * 1.8 = $10.8.

This problem has been solved

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