IS-LM Analysis. Math 202. Brian D. Fitzpatrick. Duke University. February 14, 2018 MATH

Transcription

1 IS-LM Analysis Math 202 Brian D. Fitzpatrick Duke University February 14, 2018 MATH

2 Overview Background History Variables The GDP Equation Definition of GDP Assumptions The GDP Equation with Assumptions The Liquidity-Money Equation Equation and Assumptions The IS-LM Model Definition and Observation IS-LM Analysis via Cramer s Rule Conclusion

3 Background History Idea The IS-LM Keynesian model is a linear model for a closed economy. Developed by economist John Hicks ( ) in 1937.

4 Background History Idea The IS-LM Keynesian model is a linear model for a closed economy. Developed by economist John Hicks ( ) in Throughout the 20th century considered one of the most important tools in macroeconomics.

5 Background History Idea The IS-LM Keynesian model is a linear model for a closed economy. Developed by economist John Hicks ( ) in Throughout the 20th century considered one of the most important tools in macroeconomics. Closed economy assumes no imports, exports, or other leakages.

6 Background History Idea The IS-LM Keynesian model is a linear model for a closed economy. Developed by economist John Hicks ( ) in Throughout the 20th century considered one of the most important tools in macroeconomics. Closed economy assumes no imports, exports, or other leakages. The initials IS-LM refer to the two linear equations in the model.

7 Background History Idea The IS-LM Keynesian model is a linear model for a closed economy. Developed by economist John Hicks ( ) in Throughout the 20th century considered one of the most important tools in macroeconomics. Closed economy assumes no imports, exports, or other leakages. The initials IS-LM refer to the two linear equations in the model. First equation relates the investment by firms to the consumption by consumers, investment-saving.

8 Background History Idea The IS-LM Keynesian model is a linear model for a closed economy. Developed by economist John Hicks ( ) in Throughout the 20th century considered one of the most important tools in macroeconomics. Closed economy assumes no imports, exports, or other leakages. The initials IS-LM refer to the two linear equations in the model. First equation relates the investment by firms to the consumption by consumers, investment-saving. Second equation represents the money market equilibrium, liquidity preference-money supply.

9 Background Variables The variables involved in the IS-LM model are the following: Y national income (GDP)

10 Background Variables The variables involved in the IS-LM model are the following: Y national income (GDP) C consumer spending

11 Background Variables The variables involved in the IS-LM model are the following: Y national income (GDP) C consumer spending I investment spending by firms

12 Background Variables The variables involved in the IS-LM model are the following: Y national income (GDP) C consumer spending I investment spending by firms G government spending

13 Background Variables The variables involved in the IS-LM model are the following: Y national income (GDP) C consumer spending I investment spending by firms G government spending r interest rate

14 Background Variables The variables involved in the IS-LM model are the following: Y national income (GDP) C consumer spending I investment spending by firms G government spending r interest rate M money supply (total amount of money in circulation)

15 The GDP Equation Definition of GDP GDP Equation The GDP is the sum of the consumption, investment, and government spending. Y = C + I + G

16 The GDP Equation Assumptions GDP Assumptions Consumption is assumed to be proportional to GDP where 0 < b < 1. C = b Y

17 The GDP Equation Assumptions GDP Assumptions Consumption is assumed to be proportional to GDP where 0 < b < 1. C = b Y The scalar b is the marginal propensity to consume.

18 The GDP Equation Assumptions GDP Assumptions Consumption is assumed to be proportional to GDP where 0 < b < 1. C = b Y The scalar b is the marginal propensity to consume. The scalar s = 1 b is the marginal propensity to save.

19 The GDP Equation Assumptions Investment Assumptions Investment is assumed to negatively correlate with interest rates where I 0 > 0 and a > 0. I = I 0 a r

20 The GDP Equation Assumptions Investment Assumptions Investment is assumed to negatively correlate with interest rates where I 0 > 0 and a > 0. I = I 0 a r The scalar I 0 is the investment when r = 0.

21 The GDP Equation Assumptions Investment Assumptions Investment is assumed to negatively correlate with interest rates where I 0 > 0 and a > 0. I = I 0 a r The scalar I 0 is the investment when r = 0. The scalar a is the marginal efficiency of capital.

22 The GDP Equation The GDP Equation with Assumptions Substituting C = b Y and I = I 0 a r into gives the equation for GDP Y = C + I + G Y = (b Y ) + (I 0 a r) + G

23 The GDP Equation The GDP Equation with Assumptions Substituting C = b Y and I = I 0 a r into gives the equation for GDP Rearranging this equation gives where Y = C + I + G Y = (b Y ) + (I 0 a r) + G s Y + a r = I 0 + G 0 < s < 1 a > 0 I 0 > 0

24 The Liquidity-Money Equation Equation and Assumptions The liquidity-money equation assumes that the money supply is a function of GDP and interest rate M = m Y + (M 0 h r)

25 The Liquidity-Money Equation Equation and Assumptions The liquidity-money equation assumes that the money supply is a function of GDP and interest rate M = m Y + (M 0 h r) The term m Y represents the demand for funds for transactions that is proportional to the size of the economy, 0 < m < 1.

26 The Liquidity-Money Equation Equation and Assumptions The liquidity-money equation assumes that the money supply is a function of GDP and interest rate M = m Y + (M 0 h r) The term m Y represents the demand for funds for transactions that is proportional to the size of the economy, 0 < m < 1. The term M 0 h r represents the demand for funds from investors for the part of their portfolio not invested in bonds, h > 0 and M 0 > 0.

27 The Liquidity-Money Equation Equation and Assumptions The liquidity-money equation assumes that the money supply is a function of GDP and interest rate M = m Y + (M 0 h r) The term m Y represents the demand for funds for transactions that is proportional to the size of the economy, 0 < m < 1. The term M 0 h r represents the demand for funds from investors for the part of their portfolio not invested in bonds, h > 0 and M 0 > 0. Rearranging the liquidity-money equation gives m Y h r = M M 0

28 The IS-LM Model Definition and Observation Definition The GDP and the liquidity-money equations are s Y + a r = I 0 + G m Y h r = M M 0 This system of equations is called the IS-LM model.

29 The IS-LM Model Definition and Observation Definition The GDP and the liquidity-money equations are s Y + a r = I 0 + G m Y h r = M M 0 This system of equations is called the IS-LM model. Observation The IS-LM model is the system A #» x = #» b where [ ] [ ] [ ] s a A = #» Y #» I0 + G x = b = m h r M M 0

30 The IS-LM Model IS-LM Analysis via Cramer s Rule Since the coefficients in the IS-LM model are parameters, row-reducing this system is difficult and involves many cases.

31 The IS-LM Model IS-LM Analysis via Cramer s Rule Since the coefficients in the IS-LM model are parameters, row-reducing this system is difficult and involves many cases. Idea Assuming A is invertible, Cramer s Rule allows us to solve A #» x = #» b with determinants.

32 The IS-LM Model IS-LM Analysis via Cramer s Rule Since the coefficients in the IS-LM model are parameters, row-reducing this system is difficult and involves many cases. Idea Assuming A is invertible, Cramer s Rule allows us to solve A #» x = #» b with determinants. I 0 + G a M M 0 h Y = = (I 0 + G)h + (M M 0 )a s a sh + am m h

33 The IS-LM Model IS-LM Analysis via Cramer s Rule Since the coefficients in the IS-LM model are parameters, row-reducing this system is difficult and involves many cases. Idea Assuming A is invertible, Cramer s Rule allows us to solve A #» x = #» b with determinants. I 0 + G a M M 0 h Y = = (I 0 + G)h + (M M 0 )a s a sh + am m h s I 0 + G m M M 0 r = = (I 0 + G)m (M M 0 )s s a sh + am m h

34 The IS-LM Model Conclusion Note In the IS-LM model, considering G and M as the free variables that can be controlled allows us to view Y and r as dependent variables determined by G, M, and the other parameters.

35 The IS-LM Model Conclusion Note In the IS-LM model, considering G and M as the free variables that can be controlled allows us to view Y and r as dependent variables determined by G, M, and the other parameters. Example Increasing either G or M results in an increase of GDP Y.

36 The IS-LM Model Conclusion Note In the IS-LM model, considering G and M as the free variables that can be controlled allows us to view Y and r as dependent variables determined by G, M, and the other parameters. Example Increasing either G or M results in an increase of GDP Y. Increasing G or decreasing M results in an increase of the interest rate r.