Finding change in lump sum taxes to boost real GDP to its full employment level.

Suppose that the economy is short of its full-employment (potential) level of GDP, assumed to be $14,000 billion, by $500 billion.

a. Assume that the marginal propensity to consume out of disposable income equals 0.8 and the tax rate, t, equals .20. Also assume that investment, government spending, exports and imports do not vary with income. Now assume that the government wants to boost real GDP to its full employment level by changing lump sum taxes. describe how large a change in lump-sum taxes, TA, is required to do so? Show your work.

b. Next suppose that there is one change in the conditions stipulated in part a: Assume that imports vary positively with income and that the marginal propensity to import out of national income is 0.3. How large a change in lump sum taxes will it take to boost real GDP to its full employment level in this case? Show your work and describe the reason your answer to b is different than your answer to a.