Question

Suppose the market for bottled water is competitive and is characterized by the following demand and supply conditions. The inverse demand and supply curves are depicted below.

Demand: Q^D = 400 – 100 P

Supply:    Q^S = 280 + 20 P (for P > 0)

Price:

Quantity:

Consumer surplus:

Producer surplus:

Suppose in anticipation of an approaching hurricane, demand rises to Q^D = 800 – 100 P. What will happen in the market, including welfare effects, as measured by consumer and producer surplus?

New price:

New quantity:

New consumer surplus:

New producer surplus:

Answer 1

Case 1

Demand: Q^D = 400 – 100 P

Supply:    Q^S = 280 + 20 P

Market equilibrium has QD = QS

400 - 100P = 280 + 20P

120 = 120P

P = $1

Q = 280 + 20 = 300 units

CS = 0.5*(max price - current price)*current quantity = 0.5*(400/100 - 1)*300 = 450

PS = 0.5*1*(280 + 300) = 290

Case 2

Demand: Q^D = 800 – 100 P

Supply:    Q^S = 280 + 20 P

Market equilibrium has QD = QS

800 - 100P = 280 + 20P

520 = 120P

P = $4.33

Q = 280 + 20*4.33 = 366.67 units

CS = 0.5*(max price - current price)*current quantity = 0.5*(800/100 - 4.33)*366.67 = 673

PS = 0.5*4.33*(280 + 366.67) = 1400.