Chapter 11.1, Problem 71AYU

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. In an economy, suppose that the equilibrium level of income (in millions of dollars) and interest rates satisfy the system of equations,

$0.06\text{y }-5000\text{r }=240$

$0.06y+6000r=900$

Find the equilibrium level of income and interest rates.

Answer to Problem 71AYU

The equilibrium level of income is 9000 and interest rates $r=0.06$.

Explanation of Solution

Given:

$0.06\text{y }-5000\text{r }=240$

$0.06y+6000r=900$

Calculation:

$0.06\text{y }-5000\text{r }=240$   -----1

$0.06y+6000r=900$   -----2

Subtracting equation 1 and equation 2 we have,

$-11000r=-660$

$r=0.06$

Using the value of r to find y using equation 2 we have,

$0.06y+6000r=900$   -----2

$0.06y+6000\left(0.06\right)=900$   -----2

$0.06y=900-360$   -----2

$0.06y=540$

$y=9000$