Two countries the US (U) and Fiji (F). Each country i E {U, F} can decide whether to impose a positive tax on the emissions of its polluting firms (t;> 0) or to impose no tax (t; = 0). We can think of a representative firm that chooses whether to produce using a polluting technology (q = P) or a clean technology (q = C). The polluting technology generates profits of (P) = 11. The clean technology generates profits of л(P) = 10 and doesn't have to pay tax. Imposing a tax of t = 1, profits of firms using polluting technology would equal profits of firms using clean. Assume that when the firm is indifferent between the two technologies, it chooses the clean technology. technology. Let us now turn to the decisions that the governments would make if they were inde- pendently choosing whether to impose a tax or not. In the US, firms using the clean technology emit a total of 0 tonnes of CO2 emissions, while firms using the polluting technology emit a total of 900 tonnes of CO2 emissions. In Fiji, firms using the clean technology emit 0 tonnes of CO2 emissions, while firms using the polluting technology emit 100 tonnes of CO2 emissions. The governments of each country care about three things: (1) how much net profits their representative firm makes, (2) how many total CO2 emissions are emitted in the world, and (3) how much tax income they receive. In particular, let Ti(qi) denote the profits of the representative firm in country i when it chooses technology qi and E(qu, qF) = Eu (qu)+Ef(qf) the total CO2 emissions in the world. Then each country's payoffs are given by: Uu (qu, qF, E) 1000 × [TU (qu) — TU] − E(qu, qF) + 1000 × TU UF (qu,qF, E) = πF(qF) — TF – 100 × E(qu,qF) + TF - Ti = 2 and no tax Suppose that each country can choose between a lump-sum tax of Ti = 0. Countries can only impose taxes on their own firms, not on the firms of the other countries. 1. Using the firm's behaviour given different tax levels, calculate the profit and emissions under the following scenarios. (a) Only the US imposes a tax: TU (b) Only Fiji imposes a tax: Tf = 2, tu = 0. (c) Both countries impose a tax: Tu = TF = 2. (d) Neither country imposes a tax: TU = TF = 0. = : 2, TF = 0. 2. Using these results, Represent the interaction between the two governments as a static game: who are the players, what are their actions, and what are the payoffs (you should use a table to show the payoffs)