Answer to Question #162105 in Macroeconomics for SYEDA ZAINAB

Question

The demand and supply functions for three goods are given as follows:

D_x=100-3P_x+P_y+3P_z

D_y=80 +P_x-2P_y-2P_z

D_z=120+3P_x-P_y-4P_z

S_x=-10+P_x

S_y=-20=3P_y

S_z=-3+2P_z

Q1: Determine the equilibrium prices and quantities of all three goods.

·  The government decides to:

a.  Impose a 25% tax on X

b.  Impose a 5Rs unit Tax on Y

c.  Gives a 10% subsidy on good Z

· Analyze the impact of each of these three policies separately on equilibrium prices and Quantities.

·  Also calculate changes in consumer and producer surpluses and the amount of revenue earned by the government.

Q2: Repeat this exercise when polices (a, b),(b,c) & (a, b,c) are jointly implemented. Which policy choice is best? Why?

Q:3 Provide theoretical justification (using diagrams) of all results obtained.

 

Answer 1

Q1. Q=S

100-3P _x + P _y + 3P _z = -10 + P _x

110=4Px-Py-3Pz

80 +P_x-2P_y-2P_z=-20-3P_y

100=-Py-Px+2Pz

120+3P_x-P_y-4P_z=-3+2P_z

123=-3Px+Py+6Pz

110=4Px-Py-3Pz

100=-Py-Px+2Pz

123=-3Px+Py+6Pz

Solving by the Gauss method we get the equilibrium prices

Px = 59.75 Py = -44.25 Pz= 57.75

find the equilibrium volume

S _x = -10 + P _x

S _y = -20 - 3P _y

S _z = -3 + 2P _z

S _x =49.75

S _y =-152.75

S _z = 112.5

a. if the tax is reduced by 25%, the price of the product will increase:

S _x = -10 + P _x

S _x = -10 + 1.25P _x

S _x = -10 + 62.19=52.19

Px=52.19+10=62.19

$62.19\times52.19-59.75\times49.75-=273.13$

b. the introduction of a tax on consumers will lead to a reduction in the equilibrium volume by 5 units. (-152.75– 5)=-157.75

S _y = -20 - 3P _y

-157.75=-20-3Py

-137.75=3Py

Py=-45.91

Sy=-20-132.75=-157.75

$(-)45.91\times(-157.75)-44.25\times(-)152.75-=483.12$

c. after the introduction of the subsidy

S _z = -3 + 2P _z

S _z = -3 + 2*1.1P _z=3 + 2.2P _z=244.5

Pz=123.75

$123.75\times244.5-57.75\times112.5=23760$

Q2.

(a,b)

100-3P _x + P _y + 3P _z = -10 + P _x

100-3.75P _x + P _y-5 + 3P _z = -10 + 1,25P _x

105=5Px-Py-3Pz

80 +P_x-2P_y-2P_z=-20-3P_y

80 +1.25P_x-2(P_y-5)-2P_z=-20-3(P_y-5)

80 +1.25P_x-2P_y+10-2P_z=-20-3P_y+15

95=-1.25Px-Py+2Pz

120+3P_x-P_y-4P_z=-3+2P_z

120+3.75P_x-P_y-5-4P_z=-3+2P_z

118=-3.75Px+Py+6Pz

105=5Px-Py-3Pz

95=-1.25Px-Py+2Pz

118=-3.75Px+Py+6Pz

Solving by the Gauss method we get the equilibrium prices

P_x = 45.8 Py = -41.75 Pz= 55.25

find the equilibrium volume

S _x = -10 + P _x

S _y = -20 - 3P _y

S _z = -3 + 2P _z

S _x =35.8

S _y =-145.25

S _z =107.5

(b, c)

100-3P _x + P _y -5+ 3.3P _z = -10 + P _x

105=3Px-Py-3.3Pz

80 +P_x-2P_y-2P_z=-20-3P_y

80 +P_x-2(P_y-5)-2.2P_z=-20-3(P_y-5)

80 +P_x-2P_y+10-2.2P_z=-20-3P_y+15

95=-Px-Py+2.2Pz

120+3P_x-P_y-4P_z=-3+2P_z

120+3Px-Py-5-4.4Pz=-3+2.2Pz

118=-3Px+Py+6.6Pz

105=3Px-Py-3.3Pz

95=-Px-Py+2.2Pz

118=-3Px+Py+6.6Pz

P_x = 92. 42 Py = -41.75 Pz= 67.58

find the equilibrium volume

S _x = -10 + P _x

S _y = -20 - 3P _y

S _z = -3 + 2P _z

S _x =82.42

S _y =-145.25

S _z =132.16

(a, b, c)

100-3P _x + P _y + 3P _z = -10 + P _x

100-3.75P _x + P _y-5+ 3.3P _z = -10 + 1.25P _x

105=5Px-Py-3.3Pz

80 +P_x-2P_y-2P_z=-20-3P_y

80 +1.25P_x-2(P_y -5)-2.2P_z=-20-3(P_y-5)

80+1.25Px-2Py+10-2.2Pz=-20-3Py+15

95=-1.25Px-Py+2.2Pz

120+3P_x-P_y-4P_z=-3+2P_z

120+3.75P_x-P_y-5-4.4P_z=-3+2.2P_z

118=-3,75Px+Py+6.6Pz

105=5Px-Py-3.3Pz

95=-1.25Px-Py+2.2Pz

118=-3,75Px+Py+6.6Pz

P_x = 45.8 Py = -41.75 Pz= 50.23

find the equilibrium volume

S _x = -10 + P _x

S _y = -20 - 3P _y

S _z = -3 + 2P _z

S _x =35.8

S _y =-145.25

S _z =97.45

the best option is with a subsidy for the consumer, since prices are reduced for the consumer, and it is better for the manufacturer to evade taxes