Question

 

1. P_d =200-2Q² and P_e=2Q² +4Q+32

a) find the price and market balance amount of each pair of algebraic demand and offer functions

b) draw each market balance in item (a) into one diagram

c) based on prices and the amount of market equilibrium in item (a) above, calculate the value of excess consumers and excess producers

2. P_d=60-3Q² and P_e=Q²+4Q+12

a) find the price and market balance amount of each pair of algebraic demand and offer functions

b) draw each market balance in item (a) into one diagram

c) based on prices and the amount of market equilibrium in item (a) above, calculate the value of excess consumers and excess producers

Answer 1

1. Pd =200-2Q2  

Pe=2Q2 +4Q+32

For this market:

a) Price and Market balance amount means equilibrium price and quantity where market balance:

Demand = Supply (offer curve)

200-2Q2 = 2Q2 +4Q+32

4Q2 +4Q-168= 0

4(Q2 +Q-42)=0

Q2 +7Q-6Q-42=0

Q(Q+7)-6(Q+7)=0

(Q-6)(Q+7)= 0

Q= 6 or -7

Quantity can not be negative. SO

Q*= 6

Pd =200-2Q2  = 200-2x36= 128

P*= 128

b) Pd =200-2Q2

Intercept on Y axis: When Q=0, Pm= 200

Price	0	200
Q	10	0

Pe=2Q2 +4Q+32

Intercept on Y axis: When Q=0, Ps= 32

c)  calculate the value of excess consumers and excess producers:

Excess consumers(consumer surplus)= Area in yellow= 1/2 x (200-128)(6)= 72 x 3= 216

Excess producer(producer surplus)= Area in green= 1/2 x (128-32)(6)= 96 x 3= 288

2. Pd=60-3Q2 and Pe=Q2+4Q+12

For this market:

a) Price and Market balance amount means equilibrium price and quantity where market balance:

Demand = Supply (offer curve)

60-3Q2 =Q2+4Q+12

4Q2+4Q-48= 0

Q2+Q-12= 0

Q2+4Q-3Q-12= 0

Q(Q+4)-3(Q+4)=0

Q= 3 or -4

Quantity can not be negative. So

Q*= 3

Pd=60-3Q2 = 60-3x9= 60-27= 33

P*= 33

b) Pd=60-3Q2

Intercept on Y axis: When Q=0, Pm= 60

Price	0	60
Q	4.47	0

Pe=Q2+4Q+12

Intercept on Y axis: When Q=0, Ps= 12

c)

calculate the value of excess consumers and excess producers:

Excess consumers(consumer surplus)= Area in yellow= 1/2 x (60-33)(3)= 27 x 1.5= 40.5

Excess producer(producer surplus)= Area in green= 1/2 x (33-12)(3)= 21 x 3= 31.5