Chapter 13, Problem 2PA

(a)

To determine

The IS-LM curve of the economy.

Explanation of Solution

The IS-LM curves of the economy can be calculated from the given details. It is given that the value of $\text{C}=\text{50}+0.75\left(\text{Y}-\text{T}\right)$, $\text{I}=200-20\text{r}$, $\text{NX}=200-50\in$, $\frac{\text{M}}{\text{P}}=\text{Y}-40\text{r}$, $\text{G}=200$, $\text{T}=200$, $\text{M}=3,000$, $\text{P}=3$ and $\text{r*}=5$. In order to obtain the IS curve of the economy, the goods market equilibrium should be obtained through clearing the goods market of the economy as follows:

$\begin{array}{c}\text{Y}=\text{C}\left(\text{Y}-\text{T}\right)+\text{I}\left(\text{r*}\right)+\text{G}+\text{NX}(\in )\\ =50+0.75\left(\text{Y}-\text{T}\right)+200-20\text{r}+200+200-50\in \\ =50+0.75\text{Y}-\left(0.75\times \text{200}\right)+200-\left(20\times 5\right)+200+200-50\in \\ \text{Y}-0.75\text{Y}=50+150+200-100+200+200-50\in \\ 0.25\text{Y}=400-50\in \\ \text{Y}=\frac{400-50\in }{0.25}\\ =1,600-200\in \end{array}$

Similarly, the LM curve of the economy can be obtained by equating the money market as follows:

$\begin{array}{c}\frac{\text{M}}{\text{P}}=\text{L}\left(\text{r*,Y}\right)\\ \frac{3,000}{3}=\text{Y}-40\text{r*}\\ \text{1,000}=\text{Y}-\left(40\times \text{5}\right)\\ \text{Y}=1,000+200\\ =1,200\end{array}$

Economics Concept Introduction

Mundell - Fleming model: The Mundell Fleming model is the extended version of the  IS-LM model of the economy that incorporates the BOP into the equilibrium. Thus, it is the model that portrays the short run relationship between the nominal exchange rate of the economy, interest rate and the output.

(b)

To determine

The equilibrium exchange rate, income, and net exports.

Explanation of Solution

The equilibrium exchange rate of the economy can be calculated by equating the output (Y) from both the IS curve and the LM curve as follows:

$\begin{array}{c}\text{Y}\left(\text{IS}\right)=\text{Y}\left(\text{LM}\right)\\ 1,600-200\in =1,200\\ 200\in =400\\ \in =\frac{400}{200}\\ =2\end{array}$

Thus, the equilibrium exchange rate in the economy is 2. The equilibrium income in the economy can be calculated by substituting the value of net exports in the equation above as follows:

$\begin{array}{c}\text{Y}\left(\text{IS}\right)=\text{Y}\left(\text{LM}\right)\\ 1,600-\left(200\times 2\right)=1,200\\ 1,600-400=1,200\\ 1,200=1,200\end{array}$

Thus, the equilibrium income in the economy is equal to 1,200. The net exports in the economy can be calculated by substituting the value of the exchange rate in the net exports as follows:

$\begin{array}{c}\text{NX}=200-50\in \\ =200-\left(50\times 2\right)\\ =200-100\\ =100\end{array}$

Thus, the net exports in the economy is equal to 100.

(c)

To determine

The IS and LM curves when the government spending increases by 50.

Explanation of Solution

When there is an increase in the government spending by 50, the new IS curve can be derived as follows:

$\begin{array}{c}\text{Y}=\text{C}\left(\text{Y}-\text{T}\right)+\text{I}\left(\text{r*}\right)+\text{G}+\text{NX}(\in )\\ =50+0.75\left(\text{Y}-\text{T}\right)+250-20\text{r}+200+200-50\in \\ =50+0.75\text{Y}-\left(0.75\times \text{200}\right)+200-\left(20\times 5\right)+200+200-50\in \\ \text{Y}-0.75\text{Y}=50+150+200-100+200+200-50\in \\ 0.25\text{Y}=450-50\in \\ \text{Y}=\frac{450-50\in }{0.25}\\ =1,800-200\in \end{array}$

Since the economy has the floating exchange rate, the LM curve of the economy remains unchanged. As a result, there will be no change in the income and output of the economy. Thus, the income remains at 1,200. Therefore, the new exchange rate can be calculated as follows:

$\begin{array}{c}\text{Y}\left(\text{IS}\right)=\text{Y}\left(\text{LM}\right)\\ 1,800-200\in =1,200\\ 200\in =600\\ \in =\frac{600}{200}\\ =3\end{array}$

Thus, the exchange rate is 3. A higher exchange rate decreases the exports as the domestic currency appreciates and becomes costly to the foreign countries. Thus, the increased government spending will be matched by a lower net exports. This can be illustrated as follows:

Thus, the IS curve shifts toward the right graphically, whereas the exchange rate increases.

(d)

To determine

The IS and LM curves when the government spending increases by 50 under fixed exchange rate.

Explanation of Solution

When there is an increase in the government spending by 50, the new IS equation becomes $1,800-200\in$. When the exchange rate is fixed unlike the floating one in above part, the new income can be calculated as follows:

$\begin{array}{c}\text{Y}\left(\text{IS}\right)=1,800-200\in \\ 1,800-\left(200\times 2\right)\\ 1,800-400\\ 1,400\end{array}$

Thus, when the exchange rate is fixed at 2, the equilibrium income should increase to 1,400. As a result, the money supply must be increased by the monetary authority to keep the exchange rate fixed at 2. Therefore, M would increase to 3,600 due to the rightward shift in the LM curve and it can be illustrated as follows:

Thus, the IS curve shifts toward the right increases the exchange rate, whereas the increase in the money supply leads to the rightward shift in the LM curve which brings the exchange rate back to the original position with increased output and income.