Week 9 Problem Set                                                                             Date: 6/12/2001

 1a) Y=C+I+G, Yd=Y-T, C=100+0.75Yd, I=300, T=200, G=200

         Y=100+0.75Yd+300+200

        Y=100+0.75(Y-T)+300+200

        Y=100+0.75(Y-200)+300+200

0.25Y=450

        Y=1800

∴The equilibrium output is 1800units.

 1b) 1800/3=600

        There are 600 units of labour are required to produce the equilibrium output.

        There are 100 units of labour are unemployed.

    If there is full-employment, then there are 700 units of labour,

    à700×3=2100

        ∴the full-employment output level is 2100 units.

 1c) MPC=0.75

        Government expenditure multiplier =1/(1-MPC)

                                                                 =1/(1-0.75)

                                                                 =4

When there is full-employment, ΔY=2100-1800=300

                                                        àΔG=300/4=75

 1d) MPC=0.75

        Tax multiplier =-MPC/(1-MPC)

                            =-0.75/0.25

                            =-3

When there is full-employment, ΔY=300

                                                         àΔT=300/-3=-100

1e) If increasing government expenditure,

        àG=200+75=275, T=200

        àBudget deficit (T-G)=200-275=-75

   If reducing tax,

       à G=200, T=200-100=100

        à Budget deficit (T-G)=100-200=-100

∴increasing government expenditure would be adopted.

  2a) Since the income of the elderly people is zero, the change in income is less than the young people but they still have consumption.

èΔC₂/ΔY₂>ΔC₁/ΔY₁

 2b)   Y=C+I

         =C₁+C₂+I, Y_d=Y-T, T=0, Y₂=0, I=500

        Y=300+0.8Y_d+200+0.9Y_d+500

        Y=5000 

2c)   Y=C+I, T=500

        Y=300+0.8Y-0.8(500)+200+500

        Y=3000 

Since the tax was imposed for the young people and the income is earned by they, their disposable income become lesser, i.e. their income is decreased.