Question

The market for high-quality, one-hour impression

s of President Trump can be described using the

demand and supply equations listed below. Graph thi

s market, and determine 1) the market clearing

price (P), 2) the market clearing quantity, and 3)

total economic surplus when the market clearing pri

ce

is charged.

Q

D

= 5000 – 100P

Q

S

= -1000 + 50P

Answer 1

Q^d= 5000 – 100P

Q^s= -1000 + 50P

Equilibrium price and quantity is calculated by equating Q^dand Q^s_.

5000 – 100P = -1000 + 50P

150 P=6000

P=6000/150= $40

1. Equilibrium price = $40

To find the equilibrium quantity, substitute P= $40 in either the supply or demand equation.

Substituting in Q_d= 5000 – 100P

Qd=5000-100(40)=5000-4000=1000

2. Equilibrium quantity = 1000.

To find P max, set q=0.

0=5000 – 100P

100P=5000

P=5000/100=$50

CS is the area of triangle, which is ½ x base x height

Base= equilibrium quantity-0=1000-0=1000

Height = Pmax-equilibrium price=$50-$40=$10

CS= ½ x 1000 x 10

=1/2 x 10000=$5000.

PS=

Q^s= = -1000 + 50P

Setting Q=0

0=-1000 + 50P

1000=50P

P=1000/50=$20

Base of triangle= Base= equilibrium quantity-0=1000-0=1000

Height of triangle= $40-$20=$20.

Area of triangle= ½ x base x height

=1/2 x 1000 x 20=1/2x20000

PS=$10,000

CS=$11,025.

Total welfare = PS +CS=$5000 + $10,000=$15,000.