4. Let there be H identical households._ each with endowment Y of a private good, and utility Ufrh, G) = I'll-'31 where If is the quantity of private good consumed by household In aud G the amount of public good available to all households. Let the public good be produced oneforone using the private good. (Note: this implies: MHT=IJ. Household his budget is given by 39\" + 9'" = Y1 where Y is the household's endowment and qrlLt the amount of private good that household h. voluntarily contributes toward production of the public good. a. Let all households behave competitively and take G as given. Find the equilib rium allocation of resources under voluntary provision of the public good. Is the allocation efficient? 'Why or why not? b. Can the government achieve the optimal allocation in a competitive market by providing the public good itself and nancing this with an identical lumpsum tax on each household? If so, what must the tax be?I c. Suppose that H is small enough that that households do not take G as given. That is, households see their utility function as H ft=1 and thus take in to account the effect of their choice, Iqhi on the amount of public good available. Find the symmetric (9'5 = It} for all h) equilibrium allocation when each household takes others' contributions (to. o3 for all 3' 7E h] as given