Question

The following equations represent the inverse supply and demand functions in the market for Good A: PC = 80 - ½ QD PP = 14 + QS where PC and PP are the prices paid by consumers and received by producers respectively. QD and QS are the quantities demanded and supplied, respectively.
Suppose the government is considering imposing a tax of $6 per unit of Good A.
a) (2pts) Compute the competitive market equilibrium price and output without the tax.
b) (4pts) Compute producer surplus and consumer surplus without the tax.

Answer 1

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Que) Page 1 GoodA whose demand cu ve 169 PC = 80-ID d curve is given as Taking PC-O PC-80 D=160 AD-O LOD = 80-PC QD = 160-2PC-0 Supply Curve equation is given as PP = 14+QS Talking OS : PP -14 - as opp = 14 # Tax(without) Tax equilibrium quantity and police In this case, police received by producer will be Same as pouice given by consum eu. So; PC-PS Therefore; taking eqno_ 0 and 2 80- + Q = 14+Q 66 = 0+1Q ő 2 66=3Q = 66X2 = 22x2 3 Q = 44 Ains and - puting back in eqnoz PC = 80-1044) pp=14+44 PP = 58 Ans. -80-22 PC = 58 Ans

Poice Supply curve dd Cwe Od Qty 10 20 30 409450 G 70 80 90 100 110 120 130 140 150 160170 Producer Surplus -> Asea above supply cwive and below demoacette pseiceline 50; Ps is given as - 1 x C58-140x 44 = x 44x44 PS1oduct Susplus 968 Cuoithout tax) Consum Swiplus =) Anea above puce line and below demand curve Consumers wplus = ?XC40) x ( 80-58 ) 1 x 44 x 22 = 4841 (without tax).

page-2 with Tax = $6 perunit Now stewillt Le 9+11+ Gewriting demand and Supply Curve QD = 160-2P and OS = D-14 At equilibrium, OD = QS 160-2CP++) = p-14 160 -2CP+6) =P-14 160-2P-12 P-14 160-12 + 14 = p +2P 3P = 162 p = 54 This is price Queceived by producer = $54 = PS. PS = $541 Device received ty police given /paid by buyer = $54 + $6 = $60 - PC PC = $60 Dutting PC and PS in demand S supply curve QD = 160-2060) QS = pp-14 =160-120 - 54-14 OD = 40 units OS = 40 units

Rest; C60-50 x 40 = 6X 40 =$240 is will be the government onevenue Now Producer Nweplus = I x(54-14) x 40 =+*40x 40 Producer Surplus = 800 (with tax) Conpumer Nwplus = 1 x 180-60) 40 2 = I x 20 x 40 2 Consumer Nwrplus = 400 cwith tax)