Question

Qd = 240 - 5P

Qs = P

(a) Where Qd is the quantity demanded, Qs is the quantity supplied and P is the Price. Find:

(1) the Equilibrium Price before the tax

(2) the Equilibrium quantity before the tax

(3) buyers reservation price

(4) sellers reservation price

(5) consumer's surplus before tax

(6) producer's surplus before tax

(b) Suppose that the government decides to impose a tax of $12 per unit on seller's in the market.

Determine:

(1) Demand & Supply equation after tax

(2) buyer's price after tax

(3) seller's price after tax

(4) quantity after tax

(5) consumer surplus after tax

(6) producer surplus after tax

(7) tax revenue

(8) deadweight loss of the tax

(9) total surplus after tax

Answer 1

a) Set D=S

1) 240-5P = P

P = 240/6 = 40

2) Q = 240-5*40 = 40

3) Buyers reservation price when QD = 0,

P = 240/5 = 48

4) Sellers reservation price when QS =0,

P = 0

5) CS = 0.5*40*(48-40) = 160

6) PS = 0.5*40*(40-0) = 800

b) With the tax,

1) the supply curve is QS = P+12

2) Set D=S

240-5P = P-12

240+12 = P+5P

P = 252/6 = 42

Q = 42-12 = 30

Buyers price = 42

3) Sellers price = 42-12 = 30

4) Q = 30

5) CS after tax = 0.5*30*(48-42) = 90

6) PS after tax = 0.5*30*(30-0) = 450

7) Tax revenue = 12*30 = 360

8) DWL = 0.5*(40-30)*12 = 60

9) TS = CS+PS+Revenue = 90+450+360 = 900