Technology investment 6 Consider a Cournot duopoly. The inverse demand is given by P(Q) = 8-Q where Q q1+q2 is the aggregate output. Each firm's cost is given by C(q) to 2 = cq. The marginal cost c is equal (a) Determine the Cournot equilibrium quantities and profits. Suppose that firm 1 can invest in a new technology which allows to reduce the marginal cost by 50%. That investment costs A euros to the firm (b) Determine the Cournot equilibrium when firm 1 chooses to invest in the new technol- ogy. Under which condition is it profitable for firm 1 to invest? Discuss. (c) Suppose firm 1 has invested. Find the condition under which firm 2 finds it profitable to invest in the same technology. Compare with the condition obtained in (b), and discuss Consider now the following sequential game - In a first stage, firm 1 and firm 2 decide simultaneously whether to invest or not Investment costs A and allows to reduce the marginal cost by 50%. - In a second stage, firms compete la Cournot (d) What is the relevant equilibrium concept? (e) Explain why we can rewrite the game with the following matrix form Firm 1 Firm 2 Invest Not invest (49/9 A, 49/9 - A)(64/9 - A, 25/9) (25/9,64/9 - A) Invest (36/9, 36/9) Not invest (f) Determine the equilibrium investment decisions by the firm as a function of the in- vestment cost A Technology investment 6 Consider a Cournot duopoly. The inverse demand is given by P(Q) = 8-Q where Q q1+q2 is the aggregate output. Each firm's cost is given by C(q) to 2 = cq. The marginal cost c is equal (a) Determine the Cournot equilibrium quantities and profits. Suppose that firm 1 can invest in a new technology which allows to reduce the marginal cost by 50%. That investment costs A euros to the firm (b) Determine the Cournot equilibrium when firm 1 chooses to invest in the new technol- ogy. Under which condition is it profitable for firm 1 to invest? Discuss. (c) Suppose firm 1 has invested. Find the condition under which firm 2 finds it profitable to invest in the same technology. Compare with the condition obtained in (b), and discuss Consider now the following sequential game - In a first stage, firm 1 and firm 2 decide simultaneously whether to invest or not Investment costs A and allows to reduce the marginal cost by 50%. - In a second stage, firms compete la Cournot (d) What is the relevant equilibrium concept? (e) Explain why we can rewrite the game with the following matrix form Firm 1 Firm 2 Invest Not invest (49/9 A, 49/9 - A)(64/9 - A, 25/9) (25/9,64/9 - A) Invest (36/9, 36/9) Not invest (f) Determine the equilibrium investment decisions by the firm as a function of the in- vestment cost A
