All question are with regards to the following set up. There are two firms A and B. Firms compete in a Cournot Duopoly in Karhide. They set quantities qA and qB. Inverse demand is P(qA + qB) = 18 − qA − qB and costs are C(q) = 3 ∗ q for both firms. Firm B is a domestic firm (in Karhide,) and firm A is a foreign firm (from Orgoreyn.) The government of Karhide engages in a strategic trade intervention by giving firm B a per unit subsidy of s. (That is, when firm B produces and sells qB units, firm B receives a payment of s ∗ qB from the government.) You must show your work at each step, unless the questions is followed by ”No work required.” We now consider the government’s choice of s ≥ 0. We can see from above that profits and outputs depend upon s. With that in mind, let πB(s) and qB(s) denote firm B’s profit and output as a function of the subsidy s. Let qA(s) denote firm A’s equilibrium output as a function of s. Let G(s) = πB(s) − s ∗ qB(s) denote the government’s objective function (d) Use a first order condition to find the value of s that maximizes G(s). Call this value s∗ . (e) What is qB(s∗)? How does qB(s∗) compare to the monopoly output for this market? Explain why it makes sense that qB(s∗) should take this value.
All question are with regards to the following set up. There are two firms A and B. Firms
compete in a Cournot Duopoly in Karhide. They set quantities qA and qB. Inverse demand is
P(qA + qB) = 18 − qA − qB and costs are C(q) = 3 ∗ q for both firms. Firm B is a domestic firm
(in Karhide,) and firm A is a foreign firm (from Orgoreyn.) The government of Karhide engages
in a strategic trade intervention by giving firm B a per unit subsidy of s. (That is, when firm B
produces and sells qB units, firm B receives a payment of s ∗ qB from the government.)
You must show your work at each step, unless the questions is followed by ”No work required.”
We now consider the government’s choice of s ≥ 0. We can see from above that
profits and outputs depend upon s. With that in mind, let πB(s) and qB(s) denote firm B’s profit
and output as a function of the subsidy s. Let qA(s) denote firm A’s equilibrium output as a
function of s. Let G(s) = πB(s) − s ∗ qB(s) denote the government’s objective function
(d) Use a first order condition to find the value of s that maximizes G(s). Call this value s∗
.
(e) What is qB(s∗)? How does qB(s∗) compare to the
why it makes sense that qB(s∗) should take this value.
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