Suppose an imaginary closed economy is characterized by the following: = С Ī = Co + C1 (Y – T) 400 G= 400 T = 300 = = C

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Suppose an imaginary closed economy is characterized by the following: = С Ī = Co + C1 (Y – T) 400 G= 400 T = 300 = = C is consumption, Y and Yp are, respectively, income and disposable income, T is the level of taxes, I and G, are, respectively, private investment, and government spending. Co 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 specified below. S= 0,5Y – 500
to is the autonomous tax level, and ti is the marginal tax rate. Given the values of private investment and government spending mentioned above, find the expression for the equilibrium GDP in terms of Co, C1, to and tị. (4 points) 5. Assuming that to = 200 find the value of the marginal tax rate that will yield the same level of equilibrium GDP as the one obtained (1). (4 points) 6. Find the expression for the investment multiplier in terms of cand ti and possibly Co, and to. (4 points) 7. Assume now that private investment, I, increases by 50. Find the change in GDP, AY, induced by the change in investment, AI = 50. (4 points) 8. 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 options to change its spending or to change taxes. (a) If the government changes its spending alone, find the level of AG required to coun- teract the effect on GDP of the fall in investment. (4 points) (b) If the government changes instead the level of its autonomous taxes alone, find the level of Ato required to counteract the effect on GDP of the fall in investment. Explain what happened. (4 points) (c) How does AG compare to Ato? Explain the difference, if there is any. (4 points) (d) In which direction should the government change its marginal tax rate, t1 (increase or decrease), if it uses it as the sole policy instrument to counteract the effect of the change in investment? Explain intuitively your answer. (4 points)