IS-LM Relation - Economics
Assignment #1
Deriving the IS-LM Relation
Abstract
To find the IS-LM relation for an economy defined by six structural equations, algebra is used to derive the curves and the equilibrium conditions for these curves in relation to one another. The equations show and explain that if government spending (G) increases by EUR 150 billion, consumption (C) increases by EUR 50 billion, interest rates (i) increase by 0.05 (5%), and output (Y) increases by EUR 200 billion. This causes the IS curve to shift from IS to IS '. (EconLit E270, E620, E470)
Deriving the IS-LM Relation
The structure of the goods and financial markets of an economy given in Blanchard (2006, p. 111, problem 4) is represented by the following equations:
C = 200 + 0.25YD (1)
I = 150 + 0.25 Y - 1000i (2)
G = 250 (3)
T = 200 (4)
(M/P)d = 2Y – 8,000i (5)
M/P = 1,600 (6)
Since no units of measurement are given in the problem; it will be assumed that Y, C, I, G, T, (M/P)d, and M/P are all measured in billions of US$. The interest rate i is expressed as a proportion and is measured as a decimal.
Output (Y) is:
Y = Z = C(Y-T) + I(Y,i) + G + EX - IM (7)
Since there is no mention of exports (EX) or imports (IM), it is assumed that this is a closed economy and that EX = IM = 0. The subsequent equation is modified to:
Y = Z = C(Y-T) + I(Y,i)+ G (8)
This equation (equation 8), is the formula for the IS curve. The IS curve represents all values of output (Y) and interest rate (i) where the goods market is in equilibrium. To derive the IS curve for a specific economy, substitute the functions given for C (equation 1), for I (equation 2), for G (equation 3), and for T (equation 4), to get an equation for output:
Y = Z = 200 + 0.25YD + 150 + 0.25Y – 1000i + 250 (9)
Since it is known that YD = disposable income, it is possible to substitute it for (Y – T):
Y = Z = 200 + 0.25(Y – T) + 150 + 0.25Y – 1000i + 250 (10)
As taxes (T) were given in
Deriving the IS-LM Relation
Abstract
To find the IS-LM relation for an economy defined by six structural equations, algebra is used to derive the curves and the equilibrium conditions for these curves in relation to one another. The equations show and explain that if government spending (G) increases by EUR 150 billion, consumption (C) increases by EUR 50 billion, interest rates (i) increase by 0.05 (5%), and output (Y) increases by EUR 200 billion. This causes the IS curve to shift from IS to IS '. (EconLit E270, E620, E470)
Deriving the IS-LM Relation
The structure of the goods and financial markets of an economy given in Blanchard (2006, p. 111, problem 4) is represented by the following equations:
C = 200 + 0.25YD (1)
I = 150 + 0.25 Y - 1000i (2)
G = 250 (3)
T = 200 (4)
(M/P)d = 2Y – 8,000i (5)
M/P = 1,600 (6)
Since no units of measurement are given in the problem; it will be assumed that Y, C, I, G, T, (M/P)d, and M/P are all measured in billions of US$. The interest rate i is expressed as a proportion and is measured as a decimal.
Output (Y) is:
Y = Z = C(Y-T) + I(Y,i) + G + EX - IM (7)
Since there is no mention of exports (EX) or imports (IM), it is assumed that this is a closed economy and that EX = IM = 0. The subsequent equation is modified to:
Y = Z = C(Y-T) + I(Y,i)+ G (8)
This equation (equation 8), is the formula for the IS curve. The IS curve represents all values of output (Y) and interest rate (i) where the goods market is in equilibrium. To derive the IS curve for a specific economy, substitute the functions given for C (equation 1), for I (equation 2), for G (equation 3), and for T (equation 4), to get an equation for output:
Y = Z = 200 + 0.25YD + 150 + 0.25Y – 1000i + 250 (9)
Since it is known that YD = disposable income, it is possible to substitute it for (Y – T):
Y = Z = 200 + 0.25(Y – T) + 150 + 0.25Y – 1000i + 250 (10)
As taxes (T) were given in
References: Blanchard, O. (2006). Macroeconomics (4th ed.). Upper Saddle River, NJ: Pearson Prentice Hall.