Question

Question 1 (1 point) Suppose that in a perfectly competitive market, demand is given by Q=81.0-Pand supply is given by Q=P-27.0. What is aggregate surplus in the competitive market equilibrium? No units, no rounding. Your Answer: Your Answer

Answer 1

Answer : Demand : Q = 81 - P

=> P = 81 - Q

Supply : Q = P - 27

=> P = Q + 27

At equilibrium Demand = Supply occur. So,

81 - Q = Q + 27

=> 81 - 27 = Q + Q

=> 54 = 2Q

=> Q = 54 / 2

=> Q = 27

From demand function we get,

P = 81 - 27

=> P = 54

Therefore, here the equilibrium price is $54 and quantity is 27 units.

To get the maximum willingness to pay of consumers we have to take Q = 0 for demand function. So,

P = 81 - 0

=> P = 81

Consumer surplus (C.S.) = 0.5 * Height * Base = 0.5 * (81 - 54) * 27

=> C.S. = $364.5

To get the minimum receivable payment of producers we have to take Q =0 for supply function. So,

P = 0 + 27

=> P = 27

Producer surplus (P.S.) = 0.5 * Height * Base = 0.5 * (54 - 27) * 27
=> P.S. = $364.5

Aggregate surplus = C.S. + P.S. = 364.5 + 364.5

=> Aggregate surplus = $729

Therefore, here the aggregate surplus is $729.