Question

1. Given the following information graphically illustrate the demand and supply curves and solve for the consumer and producer surplus:

a. Q(d)=200-5P     Q(s)=50+5P

b. Q(d)=1000-20P      Q(s)=200+5P

c. P=400-0.5Q(d)      P=100+0.5Q(s)

d. P=2000-2Q(d)     P=200+3Q(s)

Answer 1

(a) Qd= 200-5P

When P=0 , Qd= 200

When Qd=0 , P=40

Qs= 50+ 5P

When Qs=0, P= -10

When P=0, Qs= 50

Equilibrium is where Qd=Qs , we get:

200-5P= 50+5P

10P= 150

P= 15 (Equilibrium price)

Q= 50+5(15) = 125 (Equilibrium quantity)

Consumer surplus = (0.5)(40-15)(125) = $ 1562.5

Producer surplus = (0.5)(15-(-10))(125)= $1562.5

(b)

Qd= 1000-20P

When P=0 , Qd= 1000

When Qd=0 , P=50

Qs= 200+ 5P

When Qs=0, P= -40

When P=0, Qs= 200

Equilibrium is where Qd=Qs , we get:

1000-20P = 200+ 5P

25P= 800

P= 32 (Equilibrium price)

Q = 200+ 5(32)= 360 (Equilibrium quantity)

Consumer surplus = (0.5)(50-32)(360)= $3240

Producers surplus = (0.5)(32-(-40))(360)= $12960

(c) P= 400- 0.5Qd

When Qd=0 , P= 400

When P= 0 , Qd= 800

P= 100+ 0.5Qs

When Qs=0 , P=100

When P=0 , Qs= -200

At equilibrium Qd=Qs , we get :

400- 0.5Q = 100+ 0.5Q

Q = 300 (Equilibrium quantity )

P= 400- 0.5(300) = $250 (Equilibrium price )

Consumer surplus = (0.5)(400-250)(300)= $22500

Producer surplus = (0.5)(250-100)(300) = $22500

(d)

P= 2000- 2Qd

When Qd=0 , P= 2000

When P= 0 , Qd= 1000

P= 200+ 3Qs

When Qs=0 , P=200

When P=0 , Qs= -66.67

At equilibrium Qd=Qs , we get :

2000-2Q = 200+ 3Q

5Q = 1800

Q = 360 (Equilibrium quantity )

P= 2000- 2(360)=$1280 (Equilibrium price)

Consumer surplus = (0.5)(2000- 1280)(360)= $129600

Producer surplus = (0.5)(1280-200)(360)= $194400