Consider a simple closed economy Keynesian macroeconomic model in which consumption expenditure is a fixed proportion of national income. The proportion of national income spent on consumption is given by the marginal propensity to consume, . a. Derive an expression for the income-expenditure multiplier in this model if government expenditure is not included separately in the national accounting identity. (4 marks) b. Calculate the value of the multiplier if the marginal propensity to consume is 75 per cent. (2 marks) c. Using this multiplier, calculate national income, consumption expenditure and saving in a situation where interest rates are fixed so that investment spending is equal to $50 billion. (4 marks) d. Expand your model to include the government sector by doing the following. Include government consumption spending as a separate category in the national accounting identity. Assume that taxation is set as a fixed proportion, , of national income. Assume that household consumption is determined as a fixed proportion, , of disposable income. Derive an expression for the multiplier under these new assumptions. (6 marks) e. Calculate the value of this multiplier when = 0.25 and = 0.8. (2 marks) f. Assume that all consumption spending is done by the household sector and all investment spending is done by the corporate sector. If government spending is exogenously set at $100 billion and interest rates are set so that investment spending is equal to $50 billion, calculate the magnitudes of the following variables: national income, household consumption, houshold saving, national saving. (6 marks) g. Calculate any changes in the magnitudes of these variables in the case that investment spending falls to $25 billion. (4 marks) h. Following this fall in investment, the government raises its consumption spending to bring total expenditure back to the original level. How much must the government raise spending to achieve this? (2 marks) i. Assume that all investment is financed by borrowing. Assum