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=c0+c1(YT)

T=200I=300G=300

Cis consumption,YandYDare, respectively, income and disposable income,Tis the level of taxes,IandG, are, respectively, private investment, and government spending.

c0andc1are, 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=0.4Y400

1. FindtheequilibriumvaluesofGDP,consumption,disposableincome,andprivatesaving. (5 points)
2. Find the expression of the investment multiplier in terms ofc0and/orc1. (5 points)
3. Find the values ofc0andc1and the value of the investment multiplier (Hint: you'll probably findc0is equal to an even number, which is multiple of 6). (3 points)
4. From this question on, you must use when needed the values ofc0andc1found in the pre- vious question. Suppose now that the government tax revenue,T, has both autonomous and endogenous components, in the sense that the tax level depends on the level of in- come. T=t0+t1Y t0is the autonomous tax level, andt1is the marginal tax rate. Given the values of private investment and government spending mentioned above, find the expression for the equilibrium GDP in terms ofc0,c1,t0andt1. (5 points)
5. Assuming thatt0=100 andt1=0.1, find the new equilibrium value of GDP. (3 points)
6. Find the expression for the investment multiplier in terms ofc1andt1and possiblyc0, and t0. (3 points)
7. Assume now that private investment,I, falls from 300 to 250. Find the change in GDP, Y, induced by the change in investment,I=50. (3 points)
8. The government does not like the change in GDP induced by the fall in private invest- ment. It wants to bring it back to the level found in Question (5). 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 ofGrequired to coun- teract the effect on GDP of the fall in investment. Explain what happened. (4 points)(b)If the government changes instead the level of its autonomous spending alone, find the level oft0required to counteract the effect on GDP of the fall in investment. Explain what happened. (4 points)(c)How doesGcompare tot0? Explain the difference, if there is any. (2 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 fall in investment? Explain intuitively your answer. (3 points)