Question

The demand and supply for an unnamed product can be described by: QD = 200 – 2×PD (demand function); QS = 4×PS – 16 (supply function).
2. At the Pareto-Efficient quantity, what is the total benefit provided to buyers of all units produced and traded?
A. No more than $2,000
B. More than $2,000 but no more than $4,000
C. More than $4,000 but no more than $6,000
D. More than $6,000 but no more than $8,000
E. More than $8,000

Answer 1

Answer : The answer is option D.

Demand function : Q = 200 - 2P

=> 2P = 200 - Q

=> P = (200 - Q) / 2

=> P = 100 - 0.5Q

Supply function : Q = 4P - 16

=> Q + 16 = 4P

=> P = (Q + 16) / 4

=> P = 0.25Q + 4

The equilibrium condition is Demand = Supply occur. So,

100 - 0.5Q = 0.25Q + 4

=> 100 - 4 = 0.25Q + 0.5Q

=> 96 = 0.75Q

=> Q = 96 / 0.75

=> Q = 128

From the demand function we get,

P = 100 - (0.5 * 128)

=> P = 36

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

P = 100 - (0.5 * 0)

=> P = 100

Consumer surplus (C.S.) = 0.5 * Height * Base = 0.5 * (100 - 36) * 128 = $4,096

Now to obtain the minimum acceptable price for producers we have to take Q = 0 for supply function. So,

P = (0.25 * 0) + 4

=> P = 4

Producer surplus (P.S.) = 0.5 * Height * Base = 0.5 * (36 - 4) * 128 = $2,048

Total surplus = Consumer surplus + Producer surplus = $4,096 + $2,048 = $6,144

Therefore, here the total benefit is higher than $6,000 but less than $8,000. So, the option D is correct.