Suppose the following aggregate expenditure model describes the US economy:
C = 1 + (8/9)Yd T = (1/4)Y I = 2 G = 4 X = 3 IM = (1/3)Y where C is consumption, Yd is disposable income, T is taxes, Y is national income, I is investment, G is government spending, X is exports, and IM is imports, all in trillions $US.
(a) Derive a numerical expression for aggregate expenditure (AE) as a function of Y. Calculate the equilibrium level of national income. Illustrate in a diagram with AE on the vertical and Y on the horizontal axis. [Hint: While solving, do not convert the fractions to decimals.] 
(b) Calculate the equilibrium levels of consumption spending and private saving (S) [Hint: Recall that C and S are functions of disposable income.]. Is the government running a surplus or deficit? Does the country have a trade surplus or deficit? 
(c) Now imagine that as a result of a world-wide financial crisis, both investment and exports decrease by 1 each. What is the new level of national income? Illustrate the effects in your diagram. What is effect on the government’s budget? [Hint: Using the multiplier simplifies the calculations.] 
(d) The government decides to use an increase in government spending to restore national income to its original level. By how much would it have to increase spending? What happens to the government’s budget balance? Explain why the government’s deficit does not increase by the full amount of the increase in spending. 
please use diagrams where appropriate
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