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suggested solutions to midterm exam (part b&c)

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                                  YORK UNIVERSITY
                                   Atkinson College
                               Department of Economics
                            ECON 2450 - Midterm Examination
                                     July 13, 2006

                     Suggested Solutions to Part B and Part C

Part B                 Short Questions                                                [15 marks]
Each question is worth 7.5 marks.

Answer two of the following three questions in the answer booklet.

Use diagrams and/or numerical examples where appropriate. Unsupported answers will
receive no marks. It is the explanation that is important.

B1.    Using the debt-deflation theory, explain the effects of expected deflation on
       equilibrium income, nominal interest rate and real interest rate.

According to the debt-deflation theory, an expected deflation will lead to a decrease in
equilibrium income, a fall in nominal interest rate and a rise in real interest rate. See Figure 11-8
and pages 319 and 320 of the textbook for an explanation.


B2.    Graphically derive the aggregate demand curve with the IS-LM model. Explain why
       the aggregate demand curve slopes downward.

See Figure 11-5 and pages 311 and 312 of the textbook.


B3.    Explain whether the following statement is True, False or Uncertain.

       a.      In a small open economy, fiscal policy is effective.

The statement is uncertain because in a small open economy under floating exchange rates fiscal
policy is ineffective but under fixed exchange rates it is effective.

 See Figure 12-6 and pages of 339-340 of the textbook for an explanation of the case of floating
exchange rates and see Figure 12-11 and pages of 347-348 of the textbook for an explanation of
the case of fixed exchange rates.
                                                                                     Page 2 of 8 Pages



Part C                        Problem Solving Questions                         [60 marks]
Answer three of the following four questions in the answer booklet. Each question is worth 20
marks

Read each part of the question very carefully. Answer all parts of the question and show all
steps of your calculations to get full marks. Use diagrams where required.


C1.    Assume that the long-run aggregate supply curve is vertical at Y = 3,000 while the short-run
       aggregate supply curve is horizontal at P = 1.0. The aggregate demand curve is Y = 3(M/P)
       and    M = 1,000.


      a. If the economy is initially in long-run equilibrium, what are the values of P and Y?
         Illustrate your answers in a diagram.

         The initial long-run equilibrium price is P1=1, because at this price aggregate demand is Y =
         3*(M/P) = 3*(1000/1) =3000, which equals the long-run aggregate supply, Y= 3000. So, the
         initial long-run equilibrium price, P1=1 and output, Y1=3000.

         At the long-run equilibrium, SRAS, LRAS and AD curves intersect at the same point. In
         Figure C1-1, point E1 shows the initial long-run equilibrium, where SRAS1, LRAS1 and AD1
         intersect.


      b. Now suppose a supply shock moves the short-run aggregate supply curve to P = 1.5.
         What are the new short-run P and Y? Illustrate your answers in a diagram.

         Since the new short-run supply curve is horizontal at P2 = 1.5, the new short-run equilibrium
         output is pinned down by the value of aggregate demand at P2=1.5.

         At P2=1.5, aggregate demand is Y = 3*(M/P) = 3*(1000/1.5) =2000. So, the new short-run
         equilibrium price, P2=1.5 and output, Y=2000.

         At the short-run equilibrium, SRAS and AD curves intersect at the same point. In Figure C1-1,
         point E2 shows the new short-run equilibrium, where SRAS1 and AD1 intersect.

      c. If the aggregate demand curve and long-run aggregate supply curve are unchanged,
         what are the long-run equilibrium P and Y after the supply shock? Illustrate your
         answers in a diagram.

         In Figure C1-2, the economy starts at the initial long-run equilibrium at E1. The short-run
         aggregate supply curve shifts upward from SRAS1 to SRAS2 because of a supply shock and the
         economy moves to a new short-run equilibrium at E2. The new short-run equilibrium output
         (2000) is lower than the long-run equilibrium output (3000). That is, relative to the long-run
         equilibrium output level there is a shortage of aggregate demand at E2. As a result, price
         gradually falls to remove this shortage of aggregate demand. As the price falls, the short-run
                                                                                 Page 3 of 8 Pages

    aggregate supply curve shifts downward and the economy moves downward along the
    aggregate demand curve, AD1. Ultimately in the long-run, the economy moves back to its
    original equilibrium at E1. So, after the supply shock the long-run equilibrium price, P1=1 and
    output, Y1=3000.

    At the long-run equilibrium, SRAS, LRAS and AD curves intersect at the same point. In
    Figure C1-2, point E1 shows the long-run equilibrium after the supply shock, where SRAS1,
    LRAS1 and AD1 intersect.

d. Suppose that after the supply shock the central bank wanted to hold output at its long-
   run level. What level of M would be required? If this level of M were maintained, what
   would be long-run equilibrium P and Y? Illustrate your answers in a diagram.

 To hold output at its long-run level after the supply shock, the central bank has to
 increase the level of M to stimulate demand. To have the aggregate demand equals 3000
 at P2 = 1.5, the level of M has to be:

         3000 = 3*(M/1.5)
         or, M = (3000*1.5)/3
         So, M = 1500.

This means that the central bank has to increase the level of M by 500 which will shift
the AD curve from AD1 to AD2, as shown in Figure C1-3.

If the level of M is maintained at 1500, that is, if AD curve stays at AD2, the economy
will move quickly from the short-run equilibrium at E2 to the new long-run equilibrium
at E3. So, the new long-run equilibrium price, P2=1.5 and output, Y2=3000.

At the new long-run equilibrium, SRAS, LRAS and AD curves intersect at the same point. In
Figure C1-3, point E3 shows the long-run equilibrium, where SRAS2, LRAS1 and AD2 intersect.
                                                                                          Page 4 of 8 Pages

C2.   Consider a closed economy to which the Keynesian-cross analysis applies. Consumption is
      given by the equation C = 200 + 2/3(Y – T), where Y represents income and T represents
      taxes. Planned investment is 300, as are government spending and taxes.
      a. If Y is 1,500, what is planned spending? What is inventory accumulation or
         decumulation? Should equilibrium Y be higher or lower than 1,500?

      If Y is 1500, Planned spending, E           = C+I+G
                                                  = 200+ 2/3(Y-T)+300+300
                                                  = 800 +2/3(1500-300)
                                                  =800+ 2/3(1200)
                                                  =800+800
                                                  =1600

      So, at Y=1500, planned spending is 1600.



      Since at Y=1500, planned spending (1600) is higher than current output, there will be unplanned
      inventory decumulation. The amount of inventory decumulation = (E-Y) = (1600-1500) = 100.

      At Y=1500, firms meet the excess demand by supplying goods from their inventories, resulting
      into an unplanned reduction in their stock of goods. Firms would respond to this decline in
      inventories by producing more goods. So, the equilibrium Y must be higher than 1500.

      b. What is the planned expenditure function? What is equilibrium level of income?
      Show your results in a diagram clearly indicating the intercepts and equilibrium values.

      The planned expenditure function, E         = C+I+G
                                                  =200 +2/3(Y-T)+300+300
                                                  = 800 + 2/3(Y-300)
                                                  = 800 +2/3Y -200
                                                  = 600 + 2/3Y

      So, the planned expenditure function, E, is 600 +2/3Y

      If Y is 0, E = 600. So, the vertical intercept (E-intercept) of the expenditure function is 600.

      The equilibrium condition:          Y=E
                                          or, Y = 600 +2/3Y
                                          or, Y-2/3Y = 600
                                          or, 1/3Y = 600
                                          or, Y = 1800

      So, equilibrium level of income is 1800. In Figure C2-1, the point A shows the equilibrium.
                                                                                Page 5 of 8 Pages

c. What are equilibrium consumption, private saving, public saving, and national saving?

The equilibrium consumption, C = 200 + 2/3(Y-T)
                               = 200 + 2/3 (1800-300)
                               = 200 + 2/3(1500)
                               = 1200

So, the equilibrium consumption is 1200.

The equilibrium private saving, SP = Y-C-T
                                   = 1800-1200-300
                                   = 300

So, the equilibrium private saving is 300.

The equilibrium public saving, SG = T-G
                                  = 300–300
                                  =0

So, the equilibrium public saving is 0.



The equilibrium national saving, S = Y-C-T
                                  = 1800-1200-300
                                  = 300

So, the equilibrium national saving is 300.


d. How much does equilibrium income decrease when G is reduced to 200?
   What is the multiplier for government spending?

The government spending multiplier     = 1/(1-MPC)
                               = 1/(1-2/3)
                               = 1/(1/3)
                               =3

So, the government spending multiplier is 3. We can use this multiplier to find the change in
the equilibrium income.

Change in equilibrium income      = Government spending multiplier * Change in G
                                  = 3* (-100)
                                  =-300.

So, the equilibrium income decreases by 300 when G is reduced to 200.
                                                                                    Page 6 of 8 Pages

C3.   Assume that an economy is characterized by the following equations:

          C = 100 + (2/3)(Y – T)
          T = 600
          G = 500
          I = 800 – (50/3)r
            d
          M /P = 0.5Y – 50r

      The money supply M is 1,200 and the price level P is 1.

      a. Derive the equation for the IS curve, expressing Y as a function of r alone.
         Plot it in a diagram clearly indicating the intercepts.

      The IS curve can be derived from the goods market clearing condition:
                                   Y=E
                               or, Y = C+I+G
                               or, Y = 100 +(2/3)(Y-T)+800-(50/3)r+500
                               or, Y = 1400 +(2/3)(Y-600) –(50/3)r
                               or, Y = 1400 +(2/3)Y-400-(50/3)r
                               or, 1/3Y = 1000-(50/3)r
                               or, Y = 3000-50r

      So, the equation for the IS curve: Y = 3000-50r           (1)
       If r = 0, equation (1) implies that Y = 3000. So, the Y-intercept is 3000.

       If Y = 0, from equation (1) we get,
                                     0 = 3000-50r
                                     or, 50r = 3000
                                     or, r = 3000/50 = 60
       So, the r-intercept is 60.

      The IS curve is plotted in Figure C3-1.



      b. Derive the equation for the LM curve, expressing Y as a function of r alone.
         Plot it in a diagram clearly indicating the intercepts.

      The LM curve can be derived from the money market clearing condition:

                                (M/P)s = (M/P)d
                                or, (1200/1) = 0.5Y-50r
                                or, (1/2)Y = 1200+50r
                                or, Y = 2400+100r

       So, the equation for the LM curve: Y = 2400+100r                (2)

       If r = 0, equation (2) implies that Y = 2400. So, the Y-intercept is 2400.

       If Y = 0, from equation (2) we get,
                                                                               Page 7 of 8 Pages


                                   0 = 2400+100r
                                   or, 100r = -2400
                                   or, r = -2400/100 = -24
 So, the r-intercept is -24.

The LM curve is plotted in Figure C3-1.


c. Solve for the equilibrium values of Y and r. Now, suppose that money supply is raised
   from 1200 to 1400. How much does the LM curve shift? What are the new equilibrium
   interest rate and level of income? Illustrate your results in a diagram.

    To find the equilibrium values of Y and r, we have to find such Y and r at which both the
    money market and goods market clear. That means, we have to solve equation (1) and (2)
    simultaneously to find the equilibrium values of Y and r.

    Combining equation (1) and (2) we get,

                          3000-50r = 2400+100r
                          or, 150r = 600
                          or, r = 600/150 = 4

    So, the equilibrium value of r is 4.

    Substituting r = 4 into the LM equation (2),

                  Y = 2400+100*4
                    = 2400 + 400
                    = 2800

    So, the equilibrium value of Y is 2800. The equilibrium values of Y and r are shown in Figure
    C3-1.

M is raised from 1200 to 1400. With this new level of M, the money market clearing condition
becomes:         1400 = 0.5Y-50r
                 or, 0.5Y = 1400 +50r
                 or, Y = 2800 +100r

 So, the equation for the new LM curve: Y = 2800+100r             (3)

 If r = 0, equation (3) implies that Y = 2800. So, the Y-intercept is 2800.

 If Y = 0, from equation (2) we get,
                               0 = 2800+100r
                               or, 100r = -2800
                               or, r = -2800/100 = -28
 So, the r-intercept is -24.

This means that the LM curve shifts right by the horizontal distance of 400 or downward by the
vertical distance of 4. The new LM curve is plotted in Figure C3-1.
                                                                                      Page 8 of 8 Pages




      We have to solve equation (1) and (3) simultaneously to find the new equilibrium values of Y and r.

      Combining equation (1) and (3) we get,

                                 3000-50r = 2800+100r
                                 or, 150r = 200
                                 or, r = 200/150 = 1.33

      So, the equilibrium value of r is 1.33.

      Substituting r = 1.33 into the LM equation (2),

                         Y = 2800+100*4
                           = 2800 + 133.33
                           = 2933.33

           So, the new equilibrium value of Y is 2933.33. The new equilibrium values of Y and r are also
           shown in Figure C3-1.



       d. Derive and graph an equation for the aggregate demand curve, expressing Y as a
          function of P alone. What happens to this aggregate demand curve if monetary policy
          changes as in part (c)?

       Answer to this question will be posted soon.


C4.   Use the Mundell-Fleming model to predict what would happen to aggregate income, the
      exchange rate, and the trade balance under both floating and fixed exchange rates in response
      to each of the following circumstances:


       a. The central bank decreases money supply.

       b. A stock market boom.

       c. A wave of credit-card fraud increases the frequency with which people make transactions
          in cash.

      Use graphs to illustrate your answers.


       Answer to this question will be posted soon.

				
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