Q. 71 - Precalculus Enhanced with Graphing Utilities

Question

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

$$\begin{gathered} 0.06Y - 5000r = 240 \\ 0.06Y + 6000r = 900 \end{gathered}$$

Step-by-Step Solution

Answer

The values are $r=0.06, Y=9000$

Step 1: Given information

Our given equations are

$$\begin{gathered} 0.06Y - 5000r = 240 \\ 0.06Y + 6000r = 900 \end{gathered}$$

Step 2: Solve the equations

We get,

$$\begin{gathered} -0.06Y + 5000r = -240 \\ 0.06Y + 6000r = 900 \end{gathered}$$

Add the equations we get,

$$\begin{gathered} 11000r=660 \\ r=0.06 \end{gathered}$$

Now we find the value of Y

$$\begin{gathered} 0.06Y-5000r=240 \\ 0.06Y-5000(0.06)=240 \\ 0.06Y=540 \\ y=9000 \end{gathered}$$

Step 3: Conclusion

The values are $r=0.06, Y=9000$