Question A: Equilibrium price is 5. Equilibrium quantity is 4. 

Question B: Pb = 5.5; Ps = 4

Question C: Buyers pay more. Sellers receive less of the price. 

Step-by-step explanation

Given: 

Supply: Qs = -6 + 2P

Demand: Qd = 24 - 4P

 

Question A:

 

Step 1: Compute for the equilibrium price. 

 

Equate Demand and Supply.

 

Qs = Qd

-6 + 2P = 24 - 4P

2P + 4P = 24 + 6

6P = 30 

P = 30/6

P = 5

 

The equilibrium price is 5 per cup of frozen custard. 

 

Step 2: Compute for the equilibrium quantity. 

 

Substitute P = 5 to the demand and supply functions. 

 

Qs = Qd

-6 + 2P = 24 - 4P

-6 + 2(5) = 24 - 4(5)

-6 + 10 = 24 -20

4 = 4

 

The equilibrium quantity is 4 cups of frozen custard. 

 

Question B:

 

If tax on buyers is imposed: tax = $1.5 per unit of frozen custard

 

Step 1: Solve for the price of buyers (Pb) inclusive of tax. Let Ps = price of sellers.

 

Pb = Ps + tax

Pb = Ps + 1.5

 

Step 2: Substitute Pb to the demand function. It is the demand that is affected since the tax is imposed on consumers. 

 

Qd = 24 - 4Pb

Qd = 24 - 4(Ps + 1.5)

Qd = 24 - 4Ps - 6

Qd = 18 - 4Ps

 

Step 3: Equate supply and demand.

 

Qs = Qd

-6 + 2Ps = 18 - 4Ps

2Ps + 4Ps = 18 + 6

6Ps = 24

Ps = 24/6

Ps = 4

 

The competitive equilibrium price that sellers receive is Ps = 4. 

 

Step 4: Substitute Ps = 4 to the buyer's price, Pb. 

 

Pb = 4 + 1.5 = 5.5

 

The competitive equilibrium price that buyers pay is Pb = 5.5. 

 

Step 5: Substitute Ps = 4 to the supply function. 

 

Qs = -6 + 2(4) = -6 + 8 = 2

 

The competitive equilibrium quantity is Qd = Qs = 2.

 

Question C:

 

The per-unit tax increases the buyer's price from 5 to 5.5. Consumers will have to pay more for each unit of frozen custard. The equilibrium quantity also decreases from 4 cups to 2 cups because of the tax. The sellers receive a lower price at Ps = 4 because of the tax.