Cairo University
Faculty of Economics and Political Sciences
Economics Department
Mathematical Economics II
Sheet 5: Keynesian National Income Model
1) Briefly discuss each of the following:
1- The general assumptions of the Keynesian Theory of Income Determination.
2- Marginal propensity to consume (MPC), Marginal propensity to save (MPS), and the
relationship between them.
3- The Multiplier and its relationship with MPC and MPS.
4- The impact of adding the government sector to the two-sector Keynesian model on the
multiplier and the equilibrium output.
5- The impact of adding the foreign sector to Keynesian model on multiplier and equilibrium
level of income.
6- The effect of Marginal propensity to import (MPM) on multiplier.
2) Given the following two sector model,
C = 100 + 0.8Y , I = 500
Calculate:
1- The Marginal Propensity to Consume (MPC) and the Marginal Propensity to Save (MPS).
2- The multiplier.
3- The equilibrium level of income.
4- The Average Propensity to Consume (APC) and the Average Propensity to Save (APS).
5- Rate of Change of Average Propensity to Consume (APC) and Average Propensity to Save
(APS).
6- Elasticity of output with respect to autonomous consumption and Marginal Propensity to
Consume (MPC).
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3) Given the following two sector model,
C = 50 + 0.5Y , I = 150 + 0.3Y
Calculate:
1- The Marginal Propensity to Consume (MPC) and the Marginal Propensity to Invest (MPI).
2- The multiplier.
3- The equilibrium level of income.
4) Given the simple Keynesian two sector model,
C = a + bY , I = Ī + iY
Where: C is consumption, Y is income, I is investment, a is autonomous consumption, b is
Marginal propensity to consume, Ī is the autonomous investment and i is Marginal propensity
to invest.
Derive the multiplier and the equilibrium level of income.
5) Assuming a closed economy model,
C = 80 + 0.6 (Y-T) , I = 250 , G = 120 , T = 60
Calculate:
1- The Multiplier.
2- The equilibrium level of income.
6) Given the following simple economy model,
C = 50 + 0.5 Y , I = 200
Calculate:
1- The multiplier.
2- The equilibrium level of income.
3- If Marginal Propensity to Consume (MPC) increased so that the consumption equation
became: C = 50 + 0.7Y. Re-calculate the multiplier and the equilibrium level of income,
commenting on the difference between the two cases.
4- If the government sector is added to this economy (A three- sector model) where:
The proportional income tax (r) = 0.3, Government expenditure (G) = 60, and the Marginal
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Propensity to Consume (MPC) = 0.5. Re-calculate the multiplier and the equilibrium level
of income, commenting on the difference between the two cases.
7) Given the following data,
C = 300 + 0.8 Yd , I = 1500 , G = 1200 , r = 0.2 , X = 800 , M = 0.15Y
Where Yd is the disposable income
Calculate:
1- The Marginal Propensity to Consume (MPC) and Marginal Propensity to Import (MPM).
2- The multiplier.
3- The equilibrium level of income, and determine whether it reflects a stable equilibrium or
not.
4- The Average Propensity to Consume (APC)
8) Given the following information,
C = 200 + 0.25 (Y-T), I = 300, G = 200, X = 50 + 0.125 Y, M = 100 + 0.25Y, r = 0.25
Calculate:
1- The multiplier.
2- The equilibrium level of income.
9) Given the following information,
C = 300 + 0.8 (Y-T) , I = 1500 , G = 1200 , X = 1000 , M = 500 , T =500
Calculate:
1- The multiplier.
2- The equilibrium level of income.
3- If the lump sum tax was increased to 1000, Re-calculate the multiplier and the Equilibrium
level of income, commenting on the difference between the two cases.
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10) Given the following closed model,
C = a + b Yd , Yd = Y(1-r) , I and G are exogenous variables
Where: C is consumption, Yd is the disposable income, I is investment, b is Marginal
propensity to consume, a is autonomous consumption (subsistence level), G is government
expenditure, and r is proportional income tax rate.
Derive the Multiplier and the Equilibrium level of income.
11) If you are an economic expert in a closed economy. If the Marginal Propensity to
Consume (MPC) is 0.8, and the equilibrium level of income is achieved when the value of the
multiplier is 1.5. What are the suggested government policies to reach the equilibrium
level of income?
