Question

Question 2 The Republic of Ruritania's demand for Brawndo is supplied by two firms competing a la Cournot. Firm 1 is the domestic firm, and firm 2 is the foreign firm. The inverse demand curve for Brawndo in Ruritania is given by p=1-9 where q is the total quantity of Brawndo supplied. Firm's 1 and 2 each have a constant marginal cost of 0.5 per unit. The Champagne Socialist party of Ruritania (the current ruling party) levies an import tax on firm 2 of t per unit of output sold by firm 2 in Ruritania. Note 0 <t< 0.25. 1. Write down firm l's profit as a function of 91, 92. 2. Determine firm l's reaction function. 3. Write down firm 2's profit as a function of q1, 42 and t. 4. Determine firm 2's reaction function. 5. Determine the equilibrium values of qı and q2 as a function of t. 6. Explain why the condition that t < 0.25 is needed. 7. Define domestic welfare to be the sum of consumer surplus in Ruritania, firm 1 profits and the monies raised through the import tax. If t is set to 0.2, is domestic welfare higher or lower than if there is no import tax?

Answer 1

p = 1 - q = 1 - q1 - q2 [since q = q1 + q2]

(1)

For firm 1,

Revenue (R) = p x q1 = q1 - q1² - q1q2

Cost (C) = 0.5q1

Profit (Z1) = R - C = q1 - q1² - q1q2 - 0.5q1 = 0.5q1 - q1² - q1q2

(2)

Firm 1 maximizes profit when $\dpi{80} \partial$ Z1/$\dpi{80} \partial$q1 = 0.

$\dpi{80} \partial$Z1/$\dpi{80} \partial$q1 = 0.5 - 2q1 - q2 = 0

2q1 + q2 = 0.5 [Firm 1 reaction function]

(3)

For firm 2,

Revenue (R) = p x q2 = q2 - q1q2 - q2²

Cost (C) = q2 x (0.5 + t) = 0.5q2 + tq2

Profit (Z1) = R - C = q2 - q1q2 - q2² - 0.5q2 - tq2 = (1 - 0.5 - t)q2 - q2² - q1q2 = (0.5 - t)q2 - q2² - q1q2

(4)

Firm 2 maximizes profit when $\dpi{80} \partial$ Z2/$\dpi{80} \partial$q2 = 0.

$\dpi{80} \partial$Z2/$\dpi{80} \partial$q2 = 0.5 - t - 2q2 - q1 = 0

2q2 + q1 = 0.5 - t [Firm 1 reaction function]

NOTE: As HOMEWORKLIB Answering Policy, 1st 4 parts are answered.