Check my answer please: tax, CS, PS?

Question

The demand and supply functions of cell phones in an economy are Pd = 214-5Qd, Ps = 7 + 4Qs, P is $/unit, Q=#units sold. The gov't imposes a tax of $36 per unit sold on suppliers.

(i)What is the price and quantity in the competitive equilibrium before taxes?

(ii)What is the consumer surplus, the producer surplus and the total welfare?

(iii)What is the price and quantity after the tax is imposed?

(iv)What is the consumer surplus, producer surplus and the total welfare now?

(v)Has welfare increased or decreased? What is the dead weight loss to society?

(vi)Use elasticities to show whether suppliers or buyers pay the greater burden of the tax.

(vii)How much of the tax do the consumers pay? How much do the suppliers pay?

i) so Qs = Qd @ equilib, and solving for that i got $99/unit, Q = 23 units sold

ii) graphing the rearranged eqns (Q=...) on calculator, I got CS = 23*115*.5 = 1322.5, PS = 23*99*.5 = 1138.5

Total welfare = CS + PS = 2461

iii) tax$36/unit sold: is that...

Answer 1

(i)

214-5Q=7+4Q

9Q=207

Q=23

P=214-115=99

(ii)

CS=(214-99)*23/2=115*11.5=1322.5

PS=(99-7)*23/2=1058

TW=1058+1322.5=2380.5

(iii)

P=214-5Q (demand)

P-36=7+4Q =>> P=7+36+4Q=43+4Q (supply)

For equilibrium (demand)=(supply)

So

214-5Q=43+4Q

9Q=214-43=171

9Q=171

Q=171/9

Q=19

P=119

For demand:

P=214-5Q=214-5*19=214-95=119

Or for supply:

P=43+4Q=43+4*19=43+76=119

(iv)

CS=(214-119)*19/2=902.5

PS=(119-43)*19/2=722

TaxRevenue(Welfare)=36*19=684

TW=902.5+722+684=2308.5

(v)

ΔTW=2308.5-2380.5= -72

Total welfare decreased for deadweight loss=72

The rest I will check later.

(vi)

(vii)

P.S. For equilibrium prices and quantities are the same - so they just give Pd and Ps to show you which one is equation of demand and which one is supply.