Question 1: Lindahl pricing A competitive economy has three consumers indexed a = 1,2,31. It produces two goods, a private good X and a public good G. Consumers of course choose individual amounts of X to consume, but are restricted to the same quantity of G. The ecommy has a linear ppf with slope -1, that is, X can be transformed into G at a rate of 1 for 1 (or the MRT is 1). Thus the prices of X and G are equal. Normalise the price of X to unity, then this is also the cost of producing each unit of G. In order to price the public good, the government has declared that each consumer will have to pay a unique fraction of the cost of each unit of public good provided. COnsumer e's utility function is given by: Ua(za,G)=3:a + alnG; a=1,2,3. Thus consumer 2's utility is 3:2 + 2ln G, where I put the consumer's name as a subscript to avoid confusing it with an exponent (i.e., :32 may be mistaken for :r-squared). Suppose the government assesses each consumer a liable for a fraction Ta of the cost of each unit of the public good. Thus consumer a. can \"buy\" the public good for a price 1-,, per unit. (i) Find each c0nsumer's demand for the public good. (ii) Note that the same amount of public good will be available to each consumer. Hence in equi- librium all consumers must demand the same amount. Use this to write down three equilibrium conditions, where each condition relates two of the three T's. (iii) Also in equilibrium, the prices paid by the three consumers must add up to the cost of the public good. Use this to write down a further condition. (iv) Find the equilibrium fractions Ta, and the equilibrium quantity of the public good supplied. (v) Suppose the economy has total resources enough to produce a combined 20 units of X and G.Recall that the PPF is linear with M RT = 1. So the GDP of this economy is 20. Suppose also that this GDP is distributed such that consumers 1 and 2 each have 5 units of income, while 3 has 10 units of inc0me. Write down the budget equations of the three agents, and nd how Walras' Law applies to your calculations above