Problem 4 {45 points} Note: In the following problem, it is important to show all the steps used to get your answers. Suppose an imaginary closed economy is characterized by the following: C Cad-1 {YT} thn+t1Y I : SUI] G230D C is consumption, '1' and "FD are, respectively, income and disposable income, T is the level of taxes, and I and G, are, respectiver private investment, and government spending. (:0 and c1 are, respectively, autonomous consumption and the marginal propensity to con sume; their values are unknown. However, the expression for private saving, S, is as specied below, where 51 is the marginal propensity to save out of total income. 5 =D.4YS 1. Assuming that the marginal tax rate, h, is equal to [ll and the equilibrium GDP is 2000, find the level of autonomous taxes, to, the equilibriLun values of consumption, disposable income, and private saving. (10 points) 2. Find the expression of the investment multiplier in terms of ca and;f or (:1. [5 points) 3. Find the values of C0 and c1 and the value of the investment multiplier. (5 points) 4. Assume now that private investment, 1', decreases by 50: Jill = 50. Find the change in GDP, ELY, induced by the change in investment. {5 points} 5. The government does not like the change in GDP induced by the increase in private in vestment. It wants to bring it back to the level found in Question {1). For that purpose, it has the option to change its spending or its taxes. (a) If the government changes its spending alone, nd the level of iG required to offset the impact of the decline in investment on GDP. {5 points} {b} If the government instead changes only the level of its autonomous taxes, nd the level of at.) required to offset the impact of the decline in investment on GDP . Ex plain what happened. (5 points)