Answer a$-$g clearly and draw the required graph. The Republic of Keynesia is a closed economy and obeys our short$-$run IS$-$LM model. Assume it starts out in equilibrium in both the goods market and the money market. Keynesia's economy is described by the following set of equations:

Goods market:

$C=c_0+c_1(1-t)Y,$ where C is consumption; Y is income; t represents a proportional tax; and $c_0$ and $c_1$ are positive constants.

$I=b_0-b_{1}i,$ where I is investment; $i$ is the interest rate; and $b_0$ and $b_1$ are positive constants.

$G=G,$ where $G$ is a positive constant.

Money market:

$,M^4=P(m_e+m_{1}Y-m_{2}i),$ where $M^d$ is nominal money demand; P is the price level; $m_0($a positive constant$)$ represents exogenous changes to $M^j$; and $m_1$ and $m_2$ are also positive constants.

Let $M^3$ represent nominal money supply.

$($a$)$ Derive the IS relation and the LM relation equations. $(2$ marks$)$

$($b$)$ Now let $-=\frac{1}{1-c_l(1-t)}$ for simplicity of notations. Derive the expression for aggregate demand using your answer to part $($a$).($Hint: To derive the AD curve, just substitute in for i into the IS equation from the LM equation. You will obtain an equation of Y as a function of P $.$ In the right$-$hand$-$side of AD equation, you still keep those parameters, such as $,M^8,$ etc.$)(3$ marks$)$

$($c$)$ Now let:

$c_0=200$

$c_1=0\mathrm{.}5$

$b_0=300$

$b_1=0\mathrm{.}4$

$m_0=400$

$m_1=1$

$m_2=0\mathrm{.}8$

$M^s=200$

$\frac{?}{\text{b}\text{a}\text{r}}(G)=100$

$t=0$

$Y_n=550$

Derive the AD equation using these figures. $($All figures are in millions of HK dollars.$)(3$ marks$)$

$($d$)$ Use the same conditions in part $($c$).$ Suppose the aggregate supply takes the following form: $P=P^e+(\frac{1}{50})(Y-Y_n)$ and $P=1.$ Assume we are in the short$-$run for now. What is the short run equilibrium output, $Y^{**}?$ What is the expected price level, $P^e?$ Draw and label the AS$-$AD diagram for this case and denote the short run equilibrium in this economy as point A $.$ Also denote the natural level of output in the diagram. $(4$ marks$)$

$2$

ECON $2123$: Macroeconomics

Problem Set $4$

Instructor: Fei DING

$($e$)$ If Y happened to be equal to the natural level of output $Y_n,$ what must be the relation between P and $P^{e?}(2$ marks$)$

$($f$)$ The Keynesian government is up for re$-$election soon, so it wants to achieve the natural level of output. $($We are still in the short run now.$)$ Propose two different policy options $($fiscal and monetary$)$ that would do the job. For each policy option, draw the AS$-$AD and the IS$-$LM diagrams, and show how the two diagrams are related to each other. Calculate by how much the government must increase$/$decrease government spending to achieve the natural level of output. For monetary policy, you don't need to do any calculations. What is the difference between the effects of the two policy options? $(10$ marks$)$

$($g$)$ The Keynesian government decides not to listen to you, and raises government spending by more than what's required to achieve the natural level of output. Its argument is that higher output is better. The voters apparently think so too, and the government gets re$-$elected. What happens as time passes and we get to the "medium run" equilibrium? $($You do not have to do any calculations, just draw diagrams and give some intuition$/$explanations$.)(8$ marks$)$