1. The following equations describe an economy. (Think ofC,I,G, etc., as being measured in billions andias a percentage; a 5 percent interest rate impliesi=5.) \[ \begin{aligned} C & =0.8(1-t) Y \\ t & =0.25 \\ I & =900-50 i \\ \bar{G} & =800 \\ L & =0.25 Y-62.5 i \\ \bar{M} / \bar{P} & =500 \end{aligned} \] a. What is the equation that describes theIScurve? b. What is the general definition of theIScurve? c. What is the equation that describes theLMcurve? d. What is the general definition of theLMcurve? e. What are the equilibrium levels of income and the interest rate?
Question
- The following equations describe an economy. (Think ofC,I,G, etc., as being measured in billions andias a percentage; a 5 percent interest rate impliesi=5.) a. What is the equation that describes theIScurve? b. What is the general definition of theIScurve? c. What is the equation that describes theLMcurve? d. What is the general definition of theLMcurve? e. What are the equilibrium levels of income and the interest rate?
Solution
a. The IS curve is derived from the equilibrium condition in the goods market, which is Y = C + I + G. Substituting the given equations into this condition, we get:
Y = 0.8(1-0.25)Y + 900 - 50i + 800
Solving for Y as a function of i gives the IS curve.
b. The IS curve represents all combinations of the interest rate and income level at which the goods market is in equilibrium, i.e., investment equals savings.
c. The LM curve is derived from the equilibrium condition in the money market, which is L = M/P. Substituting the given equations into this condition, we get:
0.25Y - 62.5i = 500
Solving for Y as a function of i gives the LM curve.
d. The LM curve represents all combinations of the interest rate and income level at which the money market is in equilibrium, i.e., money demand equals money supply.
e. The equilibrium levels of income and the interest rate are found by solving the IS and LM equations simultaneously. This gives the intersection point of the IS and LM curves, which represents the equilibrium in both the goods and money markets.
Similar Questions
The following equations describe an economy. (Think ofC,I,G, etc., as being measured in billions andias a percentage; a 5 percent interest rate impliesi=5.) \[ \begin{aligned} C & =0.8(1-t) Y \\ t & =0.25 \\ I & =900-50 i \\ \bar{G} & =800 \\ L & =0.25 Y-62.5 i \\ \bar{M} / \bar{P} & =500 \end{aligned} \] a. What is the equation that describes theIScurve? b. What is the general definition of theIScurve? c. What is the equation that describes theLMcurve? d. What is the general definition of theLMcurve? e. What are the equilibrium levels of income and the interest rate?
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