3) (60 Points} As you know equilibrium occurs where Y = AE. That is, where aggregate output equals planned aggregate expenditure. Remember that planned aggregate expenditure in an economy with a government is AE E C + I + G, so equilibrium is Y = C +1 + G. Houtput (Y) exceeds planned aggregate expenditure (C + I + G), there will be an unplanned increase in inventories. That means actual investment will exceed planned investment. Conversely, if C + I + G exceeds Y, there will be an unplanned decrease in inventories. Assume that LIPS is 0.2 and autonomous consumption is 75 (autonomous consumption is dened as the expenditures that consumers must make even when they have no disposable income). Assume also that government spending (G) is 200 and the government is running a balanced budget. Assume also that planned investment (I) is 150. a) Write the consumption and saving functions (equations) b) Calculate the planned aggregate expenditures at any three levels of aggregate output (income) and unplanned inventory changes accordingly. At each level of aggregate output, comment on how the rms in this economy react to unplanned inventory changes. c) Find the equilibrium level of output. (1) Show the equilibrium of output graphically. Now the government decides to build a hospital for $100. That means G increases $100 but no change in tax is assumed. e) Calculate the government spending multiplier. 1) How does this increase in G without any change in T aect your answers in a, b, c and (1 above