Question

1. In Little Town, there are two suppliers of mineral water: A and B. Mineral water is considered a homogenous good. Let pA and pB denote the price and qA and qB the quantity sold by firms A and B, respectively. Suppose that the municipality provides all the water for free, so firms don't bear any production cost. The inverse demand function for mineral water is given by P=12-1/3Q

where Q=qA + qB denotes the aggregate supply of mineral water.

1. Suppose the firms compete in quantities (production levels).
   1. Assume that firms set their output simultaneously. Compute the quantity produced by each firm, the resulting market price, p, and the firms' equilibrium profits.
   2. Assume that firm A sets its output level qA first. Then, firm B observes qA and sets its output level qB. Compute the quantity produced by each firm in this two-stage game. Also, compute the resulting market price, p, and the firms' equilibrium profits.
2. Suppose the firms compete in prices.
   1. Assume that firms set their prices simultaneously. Compute the quantity produced by each firm, the resulting market price, p, and the firms' equilibrium profits.

Answer 1

P = = 12 - @ 3 P= 12 - qA -98 a. COURNOT GANE - MCA = MCg = 0 For firm A- MCA JaA TLA = (P 12- LA - 28 LA (12-4), ЧА 12- 9B FOC: aTA = 0 > 12 - 98 12 - 98 = 3 BR : Best Response of fiem > 36 - 28 %3D 36- LA Similarly, aga = simultaneously, Solving (36-LA qA = 72-36+ LA qA = > 39A= 36 Quantity, produced by each firm. Market Pnice : p= 12- & 12- 24 %3D 3

PROFITS Page2 (p- МСя) @a %3D (4-0) 12 $ 48 (4 -0) 12 $48. Пе -

Pape 3 i. STACKELBERG GAME - : fim 8's Pofit Пe- (P - мСв)чв - MCВ)я8 :). 12-2n)0 12-2A - 28 LA FOc: 298 LA 12 - २१8 12- 2A 3 BR 18 - q A 12

Page t 18 - LA So, Maximize firm A's profit, TA s.t. BR (from pest i. BR ThA 12 - LA BR LA 12 18- LA 12 - 36-9 4 12 LA 72-36+ 9A ) 4A 2. 3 Foc: ƏTUA 6+ 21a - 4 = o 2LA 3 42A-29A > 36 = 2LA Ana = 18 qA = 18- 18 18 - LA %3D %3D 18 – 9 %3D =9 Ana 13 +9 = 27 %3D %3D Price : P = 12- Masket 12 - 27 ! P= 3

Profitz Pages TTA MA= (3-0)X 18 54 MB = (3-0) x 9 %3D %3D

b

i.

MC for both the firms = 0

At equilibrium, both firms should charge Price = Marginal Cost because if any firm charges any price above this setting, then that firm will loose the entire market share and no firm wants to bear losses by charging less than MC

So, firm A and B charges P = 0

Demand curve:

P = 12 - Q/3

Q/3 = 12

Q = 36

q_A = q_B = 18

Profits:

firm A = firm B = 0 (since P = 0)

** if you liked the answer, then please upvote. Would be motivating for me. Thanks!