Suppose initially economy is at full employment level of output, equal to $500 billion, and lump- sum tax revenues are $50 billion. Assume the mag is 0.80. A sudden rise in interest rates cause a $15 billion decrease in investment spending and a $5 billion decrease in consumption spending. (a) What will be the new levels of equilibrium output and the sizes of the effect of these changes upon equilibrium output when (i) there are no income taxes or entitlement programs such as unemployment insurance' (ii) there is an income tax (2' = 25%) and there are no entitlement programs such as unemployment insurance' (iii) there g an income tax (t = 25%) and unemployment insurance payments which increase by $10 billion when aggregate output falls by $30 billion and more. Show each situation on the single (one and the same) graph of the business cycle in (real GDP time) space. (b) Why income taxes and unemployment insurance payments are called \"the built-in stabilizers \"? Explain