The government of a given country cares about the environment and also about per-capita consumption according to some preferences represented by the utility function u(e,c), where e represents the state of the environment and c represents consumption (think of e as a measure of well-being, so higher e is better). The experts have determined that e=p(c0c), where c0 is a baseline level of consumption and p>0. (a) Write down the government maximization problem. Which is the constraint? What is the price of the environment in terms of consumption? (b) The government of a given country chose to do nothing to reduce the impact of economic activity on the environment this year (i.e. e=0 ). Environmentalists claim that the government does not care about the environment at all. Is that true? What can we say about this government's valuation of the environment? (c) Suppose that we know that u(e,c)=1c1+e, and different countries differ in their level of initial consumption, c0. Solve the optimal allocation as a function of c0. Which countries choose bundles with positive enviromental protection? Does that mean that they value the environment more? In relative or in absolute terms? (d) UN has introduced sanctions for those countries that do not fulfil their protection goals. In particular, if e0. (a) Write down the government maximization problem. Which is the constraint? What is the price of the environment in terms of consumption? (b) The government of a given country chose to do nothing to reduce the impact of economic activity on the environment this year (i.e. e=0 ). Environmentalists claim that the government does not care about the environment at all. Is that true? What can we say about this government's valuation of the environment? (c) Suppose that we know that u(e,c)=1c1+e, and different countries differ in their level of initial consumption, c0. Solve the optimal allocation as a function of c0. Which countries choose bundles with positive enviromental protection? Does that mean that they value the environment more? In relative or in absolute terms? (d) UN has introduced sanctions for those countries that do not fulfil their protection goals. In particular, if e