2) {35 points) suppose you are given the following information about a closed economy: Y = $40,000 Real GDP = Income T = $6,000 Net tax collections Spr = $1,000 + 0.1S*(Y-T) + 1,000*r Private saving function; r = real interest rate | = $5,600 2,000*r Total investment function G = $6,800 Government purchases Look carefully at the equations for private saving and total investment. Note that investment is a decreasing function of the real interest rate. That is, as the rate of interest increases, the level of desired investment (i.e. the demand for loanable funds) decreases. Also, private saving is an increasing function of both the real rate of interest and disposable income (YT). The parameter 0.15 in the saving equation, which is multiplied by disposable income, is called the marginal propensity to save (MP5) and tells us how much extra saving is generated by an increase in disposable income. a) (5 points) Give some intuition on why private saving might be increasing in the real interest rate. b) (5 points) Does this government run a deficit or a surplus? c) (5 points) What is the amount of national saving? That is, write an equation for national saving (5), showing how it depends on the interest rate. d) (5 points) Without any calculations, what are the implications of changes in the amount of government deficit/surplus for the equilibrium interest rate in the economy? Note that in this model, a reduction in investment in the economy does not change long run GDP. Here the level of GDP was given exogenously; that is, the model cannot explain changes in GDP. However, our simple model here makes predictions about changes in the composition of GDP. e) (5 points) Suppose that the government increases its purchases without increasing its tax collection. What prediction does this model make about changes in the shares of consumption, investment, and government purchases in GDP? f) (5 points) Calculate the equilibrium real interest rate in this economy. Also, if you are told that the rate of inflation in this economy is 2.5%, what is the nominal rate of interest? g) (5 points) What are the total levels of saving and investment at this rate of interest? How much of the total saving is comprised of government saving and how much is private saving