Question 1. Assume the following IS-LM model:

      Expenditure Sector                         Money Sector

      Sp   = C + I + G + NX                     M   = 700

      C     = 100 + (4/5)YD                       P    = 2

      YD  = Y - TA                                   m_d = (1/3)Y + 200 - 10i

      TA  = (1/4)Y                       

      I      = 300 - 20i

      G    = 120

      NX  = -20

      (a) Derive the equilibrium values of consumption (C) and money demand (m_d).

      (b) How much of investment (I) will be crowded out if the government increases its purchases by DG = 160 and nominal money supply (M) remains unchanged?

      (c) By how much will the equilibrium level of income (Y) and the interest rate (i) change, if nominal money supply is also increased to M' = 1,100?

Question 2. Assume the money sector can be described by these equations: M/P = 400 and m_d = (1/4)Y - 10i. In the expenditure sector only investment spending (I) is affected by the interest rate (i), and the equation of the IS-curve is: Y = 2,000 - 40i.

(a) If the size of the expenditure multiplier is a = 2, show the effect of an increase in government purchases by DG = 200 on income and the interest rate.  

(b) Can you determine how much of investment is crowded out as a result of this increase in government spending?

(c)    If the money demand equation were changed to m_d = (1/4)Y, how would your answers  in (a) and (b) change?

Question 3. Assume money demand (md) and money supply (ms) are defined as: md = (1/4)Y + 400 - 15i  and ms = 600, and  intended spending is of the form: Sp = C + I + G + NX = 400 + (3/4)Y - 10i.

Calculate the equilibrium levels of Y and i, and indicate by how much the Fed would have to change money supply to keep interest rates constant if the government increased its spending by DG = 50. Show your solutions graphically and mathematically.

Question 4. Assume the equation for the IS-curve is Y = 1,200 - 40i,  and the equation for the LM-curve is

      Y = 400 + 40i.

      (a)  Determine the equilibrium value of Y and i.

      (b)  If this is a simple model without income taxes, by how much will these values change if the government increases its expenditures by DG = 400, financed by an equal increase in lump sum taxes (DTA_o = 400)?

Question 5: Assume you have the following information about a macro model:  

    Expenditure sector:              Money sector:

     S    = - 200 + (1/5)YD             ms = 400

     TA = (1/8)Y - 40                    md = (1/4)Y + 100 - 5i

     TR = 60

     I    = 300 - 10i

     G   = 70                                 

     NX = 150 - (1/5)Y 

Calculate the equilibrium values of investment (I), money demand (md), and net exports (NX).

Question 6. Assume the following IS-LM model:

     expenditure sector:                 money sector:

     Sp   = C + I + G + NX             M  = 500

     C    = 110 + (2/3)YD                P   = 1

     YD  = Y - TA + TR                 m_d = (1/2)Y + 400 - 20i

     TA  = (1/4)Y + 20

     TR  = 80

      I     = 250 - 5i

      G   = 130

      NX = -30

(a)   Calculate the equilibrium values of investment (I), real money demand (m_d), and tax revenues (TA).

(b)   How much of investment (I) will be crowded out if the government increases spending by DG = 100?