Question

A market for baby bottles has the following supply and demand functions

qS = −6 + 3p

qD = 14 − 2p

a. Now, suppose a per unit tax of 5 were charged to the buyer. What are the equilibrium quantity, price paid by the buyer, and price received by the seller?

b. How much tax revenue is raised? How much of that tax burden is borne by the buyer?

c. Calculate the Consumer Surplus, Producer Surplus, Total Welfare Level, and Deadweight Loss associated with the tax.

Answer 1

s Qs = -6 +3P Qd = 14-2P In Equilibrium Qd = QS lu-ap =-6+3P 14+6 =3ptap 20 =SP P = 20 P =64 substituting pinto as equation D9 = -6+ 3 cu) =-6+12 = 6 units. gf ss per mit Tax on buyer, then new demand equation Qd = 14-2CP+) ad = 11-2P-10 New Qd = u-ap New Equilibrium New Qd = Qs

u-2P =- 6+3 p 4+6 = 3PtQP lo - SP P = 10 seller Receive P = $2. Subst stituting pinto as equation Qs =-6+3P =-6 + 3x2 =-6 +6 -o units. Substituting Qzo into old demandey equation Qd = 14-2P o = 14-ap 2P = 14 P = 14 Buyer puy P=87 (b) Tax Revenue = Tax & quantity aftor Tax =sxo =$0

Buyra on buyrer = – 4 = $ 3 Tax burden on seller = u-2 Price u 6 8 10 12 14 16 18 202, (0) Consumer surplus decrease by Area (A) = Area of A (A) = 1 X BXH co-sX 64 (7-4) = 3 X3

c.s =$9 Decrease in productos surplus by Area (B) = area of A = 1 XB XH =o.sx 6x (4-2) = 3x2 DWL = Area of A (A+B) x 8 x H -0.5x6x (7-2) = 345 =1s Total wethore loss is a eqread to Area of DWL.