Assuming a closed economy with price level constant, briefly show how the IS and LM curves are derived. Under what circumstances will the fiscal and monetary multipliers be each equal to zero?
The IS ( investment and savings) schedule is a locus of points giving all the combinations of interest rate and income at which the goods market is in equilibrium, ceteris paribus. The IS curve is downward sloping because as interest rates fall, investment increases, thus increasing output. The steepness of the slope depends upon the sensitivity of investment to interest rate changes. The more interest sensitive the investment, the more interest sensitive the IS curve, i.e. the flatter the IS curve.
We can derive the IS curve using algebra.
Firstly we take into consideration how the goods and services of aggregate expenditure are shown.
Aggregate expenditure: AE = C+ I + G
Consumption Function: C = a + bYd
Accounting identity: Yd = Y – T
Taxation function: T = T0 + tY
Investment function: I = I0 – hR
Government exp. Function: G = G0
We then take into account that in equilibrium, aggregate supply (Y) is equal to aggregate expenditure (AE). Y = AE
Therefore: Y = C + I + G Y = (a + bYd) + (I0 – hR) + G0 Y = a + b (Y-T) + G0 + I0 – hR Y = a + b [Y – (T0 + tY)] + G0 + I0 – hR Y = a + bY – bT0 – btY + G0 + I0 – hR
Collect Y terms: Y – bY + btY = a – bT0 + G0 + I0 – hR Y (1 – b + bt) = a – bT0 + G0 + I0 – hR Y [1 – b(1-t)] = a – bT0 + G0 + I0 – hR
Solve for Y: Y = 1/(1 – b(1-t) )(a – bT0 + G0 + I0) - h/(1 – b(1-t) )R
Solve for R: R = 1/h(a – bT0 + G0 + I0) - (1 – b(1-t) )/hY Equation of the graph of the IS curve
The LM schedule is a locus of points giving all the combinations of the interest rate and real income at which the money market is in equilibrium. The LM curve shows all the combinations of real output and interest rate such that demand for real money balances is equal to supply of real money. Along the LM curve the money market is in equilibrium. We can derive the LM curve using algebra.
Demand for money: Md = kY + L0 – lR
Supply of Money: Ms = M0/P
Equilibrium condition: Ms=Md
Therefore: M0/P = kY + L0
We can derive the IS curve using algebra.
Firstly we take into consideration how the goods and services of aggregate expenditure are shown.
Aggregate expenditure: AE = C+ I + G
Consumption Function: C = a + bYd
Accounting identity: Yd = Y – T
Taxation function: T = T0 + tY
Investment function: I = I0 – hR
Government exp. Function: G = G0
We then take into account that in equilibrium, aggregate supply (Y) is equal to aggregate expenditure (AE). Y = AE
Therefore: Y = C + I + G Y = (a + bYd) + (I0 – hR) + G0 Y = a + b (Y-T) + G0 + I0 – hR Y = a + b [Y – (T0 + tY)] + G0 + I0 – hR Y = a + bY – bT0 – btY + G0 + I0 – hR
Collect Y terms: Y – bY + btY = a – bT0 + G0 + I0 – hR Y (1 – b + bt) = a – bT0 + G0 + I0 – hR Y [1 – b(1-t)] = a – bT0 + G0 + I0 – hR
Solve for Y: Y = 1/(1 – b(1-t) )(a – bT0 + G0 + I0) - h/(1 – b(1-t) )R
Solve for R: R = 1/h(a – bT0 + G0 + I0) - (1 – b(1-t) )/hY Equation of the graph of the IS curve
The LM schedule is a locus of points giving all the combinations of the interest rate and real income at which the money market is in equilibrium. The LM curve shows all the combinations of real output and interest rate such that demand for real money balances is equal to supply of real money. Along the LM curve the money market is in equilibrium. We can derive the LM curve using algebra.
Demand for money: Md = kY + L0 – lR
Supply of Money: Ms = M0/P
Equilibrium condition: Ms=Md
Therefore: M0/P = kY + L0