\documentclass{article}
\input{1402-preamble}
\psetnum{2}
\date{2009/03/02}

\begin{document}
\begin{pset}
  \begin{problem}
    
    \begin{subproblem}
      \textbf{True.} Shifting money from currency to checking
      increases the money supply, because only a fraction of checking
      deposits need to be held in reserve. The increase in the money
      supply shifts the LM curve, lowering the interest rate.
    \end{subproblem}

    \begin{subproblem}
      \textbf{False.} As the interest rate rises, bond prices fall.
    \end{subproblem}

    \begin{subproblem}
      \textbf{False.} In a liquidity trap, the interest rate is
      already at zero. Increasing the money supply has no effect,
      because it cannot force the interest rate below zero.
    \end{subproblem}

    \begin{subproblem}
      \textbf{False.} Suppose the amount of investment depends only on
      the interest rate. Now suppose the money supply is contracted,
      shifting the LM curve to the left. Fiscal policy can restore
      income to its original equilibrium value by increasing
      government spending, shifting the IS curve to the
      right. However, at that equilibrium point, the interest rate
      will be higher, so $I$ will be different.
    \end{subproblem}

    \begin{subproblem}
      \textbf{True.} If the LM curve is steep, it requires the IS
      curve to be shifted much farther to the right to increase the
      equilibrium value of $Y$ by even a small amount. This reflects
      the fact that increasing government spending increases the
      interest rates and crowds out private investment.
    \end{subproblem}
  \end{problem}

  \begin{problem}

    \begin{subproblem}
      Money is split evenly between currency and deposits:
      \[C = D = \frac{M}{2}\]
      and the total amount of central bank money equals currency plus
      reserves
      \begin{align*}
        H &= C + R = C + \theta D\\
        1200 &= \frac{M}{2} + \frac{1}{5}\frac{M}{2} = \frac{6}{10}
        M\\
        M&= 2000\\
        C = D &= \frac{M}{2} = 1000\\
        R &= \frac{D}{5} = 200
      \end{align*}
    \end{subproblem}

    \begin{subproblem}
      At equilibrium, the money demand equals the money supply, which
      we found above, so $\frac{50}{i} = 2000$, and $i = \frac{1}{40}
      = 0.0025$
    \end{subproblem}

    \begin{subproblem}
      Now $C = \frac{3}{4}M$ and $D = \frac{1}{4}M$. So
      \begin{align*}
        H &= C + R = C + \theta D\\
        1200 &= \frac{3M}{4} + \frac{1}{5}\frac{M}{4} = \frac{4}{5}
        M\\
        M&= 1500\\
        C &= \frac{3}{4}M = 1125\\
        D &= \frac{1}{4}M = 375\\
        R &= \frac{D}{5} = 75
      \end{align*}      
    \end{subproblem}

    \begin{subproblem}
        Now at equilibrium, $\frac{50}{i} = 1500$, so $i =
        \frac{1}{30} \approx 0.0333$
    \end{subproblem}

    \begin{subproblem}
      To keep the interest rate at its initial level, the central bank
      needs to bring the money demand back to its initial level of 2000 by
      adjusting the money supply. It should choose a level of
      \begin{align*}
        H &= \frac{3}{4} \cdot 2000 + \frac{1}{4} \frac{1}{5} \cdot
        2000\\
        &= 1600
      \end{align*}
    \end{subproblem}
  \end{problem}

  \begin{problem}
    
    \begin{subproblem}
      The endogenous variables are $C$, $I$, $Y$, $M^d$, and $M^s$.
    \end{subproblem}

    \begin{subproblem}
      In the goods market equilibrium,
      \begin{align*}
        Y &= Z = C + I + G\\
        &= c_0 + c_1(Y-T) +b_0 + b_1 Y - b_2 i + G\\
        &= \frac{c_0 - c_1 T + b_0 - b_2 i + G}{1 - c_1 - b_1}
      \end{align*}

      This is the IS relation.
    \end{subproblem}

    \begin{subproblem}
      In the financial market equilibrium
      \begin{align*}
        M^d &= M^s\\
        d_1 Y - d_2 i &= P M\\
        Y &= \frac{P M + d_2 i}{d_1}
      \end{align*}

      This is the LM relation.
    \end{subproblem}
\newpage
    \begin{subproblem}
      Increasing $G$ shifts the IS curve to the right. The equilibrium
      levels of income ($Y$) and consumption ($C$) rise, as does the
      interest rate $i$. Investment may either increase or decrease,
      depending on the relative values of the coefficients $b_1$ and
      $b_2$.
      \vspace{3in}

    \end{subproblem}

    \begin{subproblem}
      Increasing $M$ shifts the LM curve to the right. The equilibrium
      levels of income ($Y$), consumption ($C$), and investment ($I$)
      increase. The interest rate $i$ decreases.
      \vspace{2in}

    \end{subproblem}
  \end{problem}
\end{pset}
\end{document}