Suppose aggregate expenditure Z = C+I+G+ (XQ) where C is consumption, I is fixed investment, G is government purchases, X is exports, and Q is imports. Assume consumption (C) depends on disposable income (YD), C = CO + CYD where co is autonomous consumption, C is marginal propensity to consume, YD = Y - T with Y as income and T as net taxes. (a) (b) (c) (d) (e) (f) For a closed economy with abundant idle resources (which implies horizontal short-run aggregate supply curve such that equilibrium is demand determined at the given price level) and fixed investment I = I at given interest rate. Derive the express for equilibrium output Yo. 0.8, = 200, G 100, C1 Assume Co 50. Calculate equilibrium output Yo and simple multipliers for Co, , G, and T. What conditions would make changes in co, , G, and T have multiplier effect on equilibrium output? How much increase in net taxes is required in order to bring equilibrium output to zero? = = :50, and T = - Suppose government purchases increase AG = 50 to G' to help you determine the new equilibrium output. = Your best friend tells you that if the government increases net taxes AT: 50 and uses that to increase government purchases AG = 50, then it would not affect equilibrium output because the increase in net taxes reduces disposable income and consumption, which is made up exactly by the increase in government purchases. Therefore, it is a "wash" when these changes simply shovel expenditure from private households to government. Explain if your friend is right or not. What roles does c play in determining the change in equilibrium output and the time it takes for the economy to reach the new equilibrium? How is it related to the idea of "leakage"? If taxes paid to the government is a constant proportion of income = tY (t can be considered as the marginal tax rate) while transfer payments received from the government is constant TR. Derive the simple multipliers for co, I, G, and TR. Why these multipliers are different from those in part (b)? Explain. = G + AG = 100. Use three different methods