Question

A perfectly competitive market is characterized by supply and demand as: Qd = 200 – 2Pd  Qs = ( −10 + 5Ps), when Ps ≥ 2

Qs=0, when Ps < 2

a. What is the equilibrium price and quantity in this market if there is no tax?

b. Suppose the government imposes a tax of $7 on this market. What is the new market quantity? What happens to the price paid by buyers (Pd ) and received by sellers (Ps )?

c. How does this tax affect Consumer and Producer surplus? You must provide both a numerical answer and discussion.

d. How much revenue does this tax generate for the government?

e. What is the overall impact of this tax on the welfare of the market? You must provide both a numerical answer and discussion.

Answer 1

Qd = 200 - 2 Pd Qs = lot sps when Ps >,2. (a) equilibrium condition (ad=as I 200-2 Pd = -105PS at equilibrium Pa = Ps =P - 200- 2 P = -1075P - 210 = 7P = P = 30 Q = 200-2P = Q = 200-2(30) = 200-60=140 equilibrium Price =P = 30 equilio num quantity 9 = 140 (6) Tax of $ 7. with Tax The demand function Qd = 200- 2 Pd Becomes Qd = 200-2(Par 7) ad = 200-Pd-14 = 186-210 equilibrium (aa-as, Noor 186-Pd = 10 +5PS Ps= Pa =P at com 186-2P = -10 + 5P

186 + 10 = 5P+ 2 P 196 = 7P - P = 196 = 28 = Ps 7 Q = -lot 5 (Ps) = -10+5 (28) = Totino a = 130 Price paid by Buyer= Ps + 7 = 28+7 = 35=Pd New market quantity (8=130 Price paid by Buyers (Par) = 35 increased by $5 Poice gecieved by Sellers (Ps ) = 28 decreased by $2. (C). 100 had --------------- 30 130 140 186 200

consumer Surfius Be Yore Tax after Tax = I (100-30) 140 - 1 (100-35) (180) - 4900 = 4225 CS decreased by 675 Producer Surfius - Be Yove Tax = 4 (38-2) (140) = + (28) (140) - 1960 after Tax = 1 (28-2) (180) = 1 (26) (130) = 1690 Ps decreased by = 270. di goverment Revenue = Tax gate * Quantity after Tax = = 7x (130) 910. GR (el overall impact. Since The Producer and consumer Suo Pices Jointly decreased by = 945 and GR is only 910. So there is market inefficiency (in Terms of dead-weight Loss of 35). D.W.C { (35-28 )(10) = 70 - 35 (wei Jave reduced)

Answer 2

SOLUTION :

a.

Qd = 200 - 2 Pd 

Qs = - 10 + 5Ps

At equilibrium, Qd = Qs = Qe and Pd = Ps = Pe   

(Qe and Pe are equilibrium quantity demanded and equilibrium price respectively)

=> 200 - 2Pd = - 10 + 5Ps

=> 200 - 2Pe = - 10 + 5Pe

=> 200 + 10 = 5Pe + 2Pe

=> 7Pe = 210

=> Pe = 30  ($)

=> Qe = 200 - 2Pe

=> Qe = 200 - 2 * 30 

=> Qe = 140 units

So, equilibrium price is 30 ($) and equilibrium quantity is 140 (units) (ANSWER).

b.

If tax of $7 is imposed , 

Price with tax paid by customer = Pd + 7 

Supplier gets price of Ps 

$7 per unit goes to Govt.

Hence,

For equilibrium, Pd = Ps = Pe and Qd = Qs = Qe

So,

200 - 2(Pd + 7) = - 10 + 5Ps

=> 200 - 2(Pe + 7) = - 10 + 5Pe

=> 186 + 10 = 5Pe + 2Pe = 7Pe

=> Pe = 196/7 = 28 ($)

=> Qe = 200 - 2(28 + 7) = 130 units.

So, equilibrium price is $28 and quantity is 130 units. (ANSWER).

However, price paid by customer = 28 + 7 = 35 ($) and price received by seller is $28 .

(ANSWER)

c.

Maximum price payable before tax = 200/2 = 100

Maximum price payable after tax = 100 - 7 = 93 

Consumer surplus will get decreased and producer surplus also gets reduced..

Decrease in consumer surplus 

= Before tax - After tax

= 0.5 * (100 - 30) * 140 - 0.5 * (100 - 35) * 130 

= 675 ($) decrease. (ANSWER).

Producer surplus decrease 

= Before tax - After tax

= 0.5 * (30 - 2)  * 140 - 0.5 * (28 - 2) * 130  

(Since minimum price for supply is $2. Below $2, supply is zero).

= 270 ($) decrease (ANSWER).

d.

Government revenue 

= Tax * Qe after tax 

= 7 * 130

= 910 ($) (ANSWER).

e.

Overall Impact :

It can be seen that consumer surplus decreased by $675 and producer surplus by $270. So total surplus loss is $945. Government gains tax revenue of $910. So there is a loss of ($945 - $910) = $35 which is a dead weight loss due to imposition of tax. This shows that tax imposition worsen the economic results. Hence, it is advisable to not impose tax until and unless conditions warrant it