Chapter 11.1, Problem 72AYU

IS-LM Model in Economics In economics, the $IS$ curve is a linear equation that represents all combinations of income $Y$ and interest rates $r$ that maintain an equilibrium in the market for goods in the economy. The $LM$ curve is a linear equation that represents all combinations of income $Y$ and interest rates $r$ that maintain an equilibrium in the market for money in the economy. In an economy, suppose that the equilibrium level of income (in millions of dollars) and interest rates satisfy the system of equations

$\{\begin{array}{l}0.05Y-\text{ 1000}r=\text{ 10}\\ 0.05Y+\text{ 800}r=\text{ 100}\end{array}$

Find the equilibrium level of income and interest rates.

To determine

To find: In economics, the IS curve is a linear equation that represents all combinations of income Y and interest rates r that maintain an equilibrium in the market for goods in the economy. The LM curve is a linear equation that represents all combinations of income Y and interest rates r that maintain an equilibrium in the market for money in the economy. Ibn an economy, suppose that the equilibrium level of income (in millions of dollars) and interest rates satisfy the system of equations,

$0.05\text{y }-1000\text{r }=10$

$0.05y+800r=100$

Find the equilibrium level of income and interest rates.

Answer to Problem 72AYU

The equilibrium level of income is 1200 and interest rates $r=0.05$.

Explanation of Solution

Given:

$0.05\text{y }-1000\text{r }=10$

$0.05y+800r=100$

Calculation:

$0.05\text{y }-1000\text{r }=10$   -----1

$0.05y+800r=100$   -----2

Subtracting equation 1 and equation 2 we have,

$-1800r=-90$

$r=0.05$

Using the value of $r$ to find $y$ using equation 1 we have,

$0.05\text{y }-1000\text{r }=10$   -----1

$0.05y-1000\left(0.05\right)=10$

$0.05y=10+50$

$0.05y=60$

$y=1200$