Question

Demand in Market 1 for X is Qd = 80 – p. Demand in Market 2 is Qd = 120 – 2p. At a price of $20, which has a larger consumer surplus?

Answer 1

Given, P = $20

Now, in market 1.where, Qd = 80 - P ...(1)

Maximum willingness to pay (WTP) .

Putting Qd = 0

0 = 80 - P => P = $80.

Now, quantity demanded at equilibrium, putting P = $20 in equation (1), then we get.

Qd = 80 - 20 => 60

Qd = 60

Now consumer surplus in market 1,

CS = 0.5 * (WTP - P) * Q

putting all required value,

CS = 0.5*(80 -20) * 60 = 0.5 * 60 *60

= 30*60 = $1800

Therefore CS in market 1 is $1800.

Now, in market 2.where, Qd = 120 - 2P ...(2)

Maximum willingness to pay (WTP) .

Putting Qd = 0

0 = 120 - 2P => 2P = 120 => P = $60

Now, quantity demanded at equilibrium, putting P = $20 in equation (2), then we get.

Qd = 120 - 2(20) => 120 - 40 => 80

Qd = 80

Now consumer surplus in market 2,

CS = 0.5 * (WTP - P) * Q

putting all required value,

CS = 0.5*(60 -20) * 80 = 0.5 * 40 *80

= 20*80 = $1600

Therefore CS in market 2 is $1600.

Thus we found that CS in market 1 is greater than in market 2.

Therefore market 1 has larger consumer surplus.