Consider an economy with two identical consumers. Each consumer has an income of L and allocates...

 

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Consider an economy with two identical consumers. Each consumer has an income of L and allocates it among two private goods, 2₁ and 2, and a public good g. The prices of the private and public goods are normalized to unity. Consumer i's preferences are given by U = Blnxi + (13) Ina + In G, where G=g¹+g² and i = 1, 2. (a) Derive consumer i's demand functions for the three goods. What is the Nash equilibrium level G of the public good? [2 marks] (b) Suppose that the social welfare function is given by W = EU. What is the efficient level G* of the public good? Explain why G and G* are not the same. [3 marks] (e) Suppose the government subsidizes the purchases of the public good at a rate s. Explain how this subsidy affects the level of private provision of the public good. What is the optimal subsidy rate s that makes the private provision equilibrium efficient? [2 marks] Consider an economy with two identical consumers. Each consumer has an income of L and allocates it among two private goods, 2₁ and 2, and a public good g. The prices of the private and public goods are normalized to unity. Consumer i's preferences are given by U = Blnxi + (13) Ina + In G, where G=g¹+g² and i = 1, 2. (a) Derive consumer i's demand functions for the three goods. What is the Nash equilibrium level G of the public good? [2 marks] (b) Suppose that the social welfare function is given by W = EU. What is the efficient level G* of the public good? Explain why G and G* are not the same. [3 marks] (e) Suppose the government subsidizes the purchases of the public good at a rate s. Explain how this subsidy affects the level of private provision of the public good. What is the optimal subsidy rate s that makes the private provision equilibrium efficient? [2 marks]