Q. 72 - 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

0.05Y - 1000r = 10

0.05Y + 800r = 100

Step-by-Step Solution

Answer

The values are $r=0.05, Y=1200$

Step 1: Given information

We are given a system of equations

0.05Y - 1000r = 10

0.05Y + 800r = 100

Step 2: Solve the equations

We have,

$-0.05Y+1000r=-10+0.05Y+800r=1001800r=90$

Therefore

$r=0.05$

Now we find the value of Y

$$\begin{gathered} 0.05Y-1000r=10 \\ 0.05Y-1000(0.05)=10 \\ 0.05Y=60 \\ Y=1200 \end{gathered}$$

Step 3: Conclusion

The values are $r=0.05, Y=1200$