Homework Assignment 3

							                            Homework Assignment #3
                           Principles of Macroeconomics
                                  Economics 112
                     Assigned: Wednesday, November 24, 1999
                          Due: Friday, December 3, 1999


1. The Multiplier Effect
       a. Consider a closed economy in which no investment or government
   spending takes place. In this economy, autonomous consumption is equal to 100
   (A = 160). The tax bill is equal to 80 (T = 80). Firms in this economy set a fixed
   price and sell as much output as people demand. If household consumption is
   equal to expenditure which is equal to output:
                       Y = Expenditure = C = A + mpc  (Y-T)
       Solve the above equation for Y when mpc = .75. Now suppose that A
   increases by A = 20. How much will Y increase? Why is the increase in Y larger
   than the increase in autonomous consumption? What is the multiplier?
       b. In Hong Kong, the government does not set some amount of taxes to be
   collected. Instead, the government collects a percentage of private income. Now,
   suppose that taxes are set equal to
                                      T=tY
   where 0< t < 1 is a fraction. Solve for output when A = 160, mpc = .75, and t =
   .20. How much are taxes? Suppose that A increases by A = 20. How much will
   Y increase? How much will taxes increase? Explain why the increase in output
   following the increase in autonomous consumption is smaller than in part A.

2. Investment Demand
      Though the British economist John Hicks developed the IS-LM model in the
   1930’s, it was based on some of the theories of another British economist, John
   Maynard Keynes (which is why this type of macroeconomic theory is called
   Keynesian economics). So far we have assumed that investment is strictly a
   (negative) function of the interest rate. However, Keynes believed that the main
   cause of business cycles is fluctuations in the optimism and pessimism of owners
   and managers of businesses. He believed that investor confidence was a major
   cause of fluctuations in expenditure on investment. Now, imagine if investment
   was a function of the real interest rate, r, and animal spirits B

                                      I = I(r,B)
                                            -+
       A decrease in B caused by pessimism will reduce investment expenditure at
   any given interest rate. For the remainder of the question assume that prices are
   fixed and firms will produce any amount of goods demanded at the given price
   level. Use the IS-LM analysis to demonstrate the effects of a wave of pessimism
   that reduces investment expenditure by I.
       a. A wave of pessimism hits China reducing the level of investment
   expenditure. Use the IS-LM model of a closed economy to graphically
   demonstrate the effects of this shock on the equilibrium interest rate and output
   level. Does this shock cause and increase, decrease, or have no effect on
   consumption? Explain.
       b. A wave of pessimism hits Canada reducing the level of investment
   expenditure. Use the ISX-LMX model of a small open economy with flexible
   exchange rates to demonstrate the effect of this shock on the equilibrium exchange
   rate and the output level. Will this increase, decrease or have no effect on
   consumption and net exports. Explain.
       c. A wave of pessimism hits Hong Kong reducing the level of investment
   expenditure. Use the ISX-LMX model of a small open economy with fixed
   exchange rates to demonstrate the effect of this shock on the equilibrium exchange
   rate and the output level. Will this increase, decrease or have no effect on
   consumption, money supply and net exports. Explain.
       d. A wave of pessimism hits Japan reducing the level of investment
   expenditure. Use the IS-LM model of a large open economy to demonstrate the
   effect of this shock on the equilibrium interest rate, exchange rate and the output
   level. Will this increase, decrease or have no effect on consumption, net foreign
   investment and net exports. Explain.

3. The Algebra of the IS-LM Model
       a. In a closed economy with no government spending or taxes (G=T=0), the
   level of consumption expenditure is
                                       C = A + mpc  Y
       while investment expenditure is given by
                                       I = B – ieir
       Firms in the short run set the price level P = 1. We can then write the demand
   for liquid assets as:
                                       M = Y - iemr
       Solve for the equilibrium interest rate and output levels as a function of the
   exogenous variables (M, A, B) and the parameter values (mpc, iei, iem). Show that
   an increase in B will lead to higher interest rates and an increase in M will lead to
   lower interest rates in the short run.
       b. In an open economy with flexible exchange rates, and no government
   spending or taxes (G=T=0), the level of consumption expenditure is given by
                                       C = 100 + .75  Y
       while investment expenditure is given by
                                       I = 100 – 200r
       while net exports are given by:
                                       NX = 10 (1-e). Firms in the short run set the
   price level P = 1. We can then write the demand for liquid assets as:
                               M = Y - 1000r
                The central bank sets money supply equal to 500 and the world real
   interest rate is rw=.10. Solve for equilibrium output, the exchange rate, net
   exports, consumption and investment. Now assume that the monetary authority
   increases the money supply by 50. Solve for the new equilibrium output, exchange
   rate, consumption, investment and net exports.