If in the closed private economy the aggregate expenditure equilibrium is 470 billion. If exports of 12 billion and imports of 12 billion are now added as well as an additional 70 billion in spending by the government and given a marginal propensity to consume of .8 please explain what will happen to the aggregate expenditure curve and what will happen to the equilibrium level of GDP.

Suppose there is an economy with consumers A, Band C, private good x, and public good G. Each consumer has income Mh, where Ma=9, Mb=12 and Mc=18. Let Px=Pg=1, and the utility function is U=(x)^2 G. Assume initialy that the public good is provided privately so that G=gA+ gB+ gC.

a. Find MRS (G,X) for these preferences. Use this to determine the efficient level of public good provision.

b. Find the Nash equilibrium contribution levels, g*h, h= A,B,C, and contrast the aggregate equilibrium private provision of G with efficient level.

c. Show that the aggregate provision of G you found in (b) would be identical if instead Ma= Mb=12 and Mc=15. what would each person's contribution be now?

d. Assume again that Ma = 9, Mb = 12, and Mc=18. Suppose that G is to be determined by majority voiting, where each individual pays 1/3 of the cost of G. First, show that each person's preferences of G are single peaked. Next, find the voiting equilibrium and determine if it is efficient (or not).

e. Now suppose that G is still to be determined by majority voting, but now each individual pays relative to their income: The cost of G for person his Mh/sigmaM. Find the new voiting equilibrium and determine if it is efficient (or not).

f. Lastly, suppose that there is a utilitarian government with W=Ua+Ub+Uc. What contribution levels would it choose for each individual? Compare your answer to b. above.