Problem 1. Keynesian Cross: The economy is described by the following functions: C110+ 0.8YD Tr = 20 Tr= 40 I 70 G = 80 NI = 30 = Q1. Express aggregate demand as a function of overall income Y. • Q2. Write down a condition that describes equilibrium in the Keynesian Cross diagram • Q3. Substitute all the information that you were given and find equilibrium output. • Q4. Find the multiplier associated with government purchases. • Q5. Suppose government purchases increase by 20. By how much would the equilibrium output increase? • Q6. Illustrate change in government purchases on the Keynesian Cross diagram. • Q7. Suppose transfers increase by 20. By how much would the equilibrium output increase? Problem 2. Keynesian Cross with proportional taxation: The economy is described by the following functions: C Tz Tr C+cYD t-Y = Tr I = i G = G Nz = N₂ where t is the tax rate. Note the difference with the setup derived in class: here, the amount of taxes collected depends positively on the gross income. Q1. Express equilibrium output as function of other variables. • Q2. Find the multiplier associated with government purchases. How does this multiplier compare with that obtained in class (i.e. for a model with lump-sum taxes?) 1 • Q3. Come up with an intuitive explanation for why the multiplier is different. Problem 3. The IS Curve: The economy is described by the following functions: C = Tr = 15 Tx = 5 = 120+ 0.8YD I = 50-5i G = 80 Na 10 Q1. Derive the IS curve • Q2. Suppose taxes in the economy go up by 5, so the new value for tazes is 10. Derive the new IS curve • Q3. Illustrate the change in the (Y, i) coordinates Problem 4. Shifts in the IS Curve: How would the following shocks affect the position of the IS curve in the (Y, i) coordinates? Will the curve shift left or right? The shocks are: A. The government reduces expenditure on national defense B. Consumers become pessimistic about their future earnings and start consuming less C. A country the US trades with experiences a recession D. The government sends stimulus checks to households E. The government introduces a new capital investment subsidy program
