1,000 people live in Jaca who consume a single private good: Guhau beer. There is only one public good in the city: the skating rink. Although the inhabitants may differ in other respects, they all have the same utility function U (Xi, G) = Xi - 100 / G, where Xi is the number of Guhau bottles consumed by a citizen i and G is the area in square meters from the skating rink. The price of the bottle of Guhau is 1 euro and the price of the track is 10 euros per square meter. All the inhabitants of Jaca have an annual income of 1,000 euros.

(a) Develop the algebraic expression for the marginal ratio of substitution between the skating rink and the Guhau beer of a typical citizen. What is the marginal cost of an additional square meter of skating rink (measured relative to beer)

(b) Since the city has only 1,000 inhabitants, all with the same marginal rate of substitution, you should be able to write the equation, which states that the sum of the absolute values of the marginal rates of substitution equals the marginal cost. Write the equation and determine the value of Gefficient in the Pareto sense.

(c) Suppose that all citizens pay equally the cost of the skating rink. The total cost of the skating rink will be equal to 10G euros. Therefore, the tax fee paid by each citizen amounts to 10G / 1,000 euros = G / 100 euros. Every year all the inhabitants of Jaca vote on the surface area of the skating rink. Everyone warns that they have to pay their share. So if the surface of the skating rink is G. The number of bottles of Guhau beer that they can consume is _____.

(d) Therefore, we can express a voter's budget constraint as Xi + G / 100 = 1,000. To decide which skating rink surface to vote for, the voter has only to determine the combinations of Xi and G that maximize his utility given his budget constraint and vote for that value of G. What is this value of G in our example

(e) If the local authorities provide the skating rink of the area demanded by the voters, will this be greater, less than or equal to the efficient area in the Pareto sense

(f) Let us suppose that the culture commission of the Jaca City Council decides to promote Aragonese culture by subsidizing local skating rinks. The Government of the Autonomous Community will pay 50% of the costs of each rink in each city. Grant will be shared equally by all the inhabitants of the Community.There are many cities like Jaca in the Autonomous Community and it is true that community taxes will suffer an increase to collect the money from the grants.But as this tax will be collected from a large number of citizens, the effect of the increase will easily go unnoticed, in this case. What is the approximate area for which the inhabitants of Jaca will vote Pisa: rewrites the budget restriction for citizens taking into account that local taxes will be reduced by half and that the cost of increasing the area of the skating rink it will also be cut in half. Then determine the combinations that maximize utility.

(g) Does this subsidy promote economic efficiency