Question

1. Assume you have the following model of the expenditure sector:

         AD = C + I + G + NX        C   = 400 + (0.8)YD                I_o   = 200          

          G   = 300 + (0.1)(Y^* - Y)  

         YD = Y - TA + TR          NX_o = - 40                   TA = (0.25)Y   TR_o = 50

1. 1. What is the size of the output gap if potential output is at Y^* = 3,000?
2. 2. By how much would investment (I_o) have to change to reach equilibrium at Y^* = 3,000, and how does this change affect the budget surplus?
3. 3. From the model above you can see that government purchases (G) are counter-cyclical, that is, G is increased as national income decreases. If you compare this specification of G with one that has a constant level of government spending (for example, G_o = 300), how would the value of the expenditure multiplier differ?
4. 4. If TR (transfer payments) increased by 100, what would be the new level of output?

Answer 1

I have answered all the parts for you. I hope it helps. Please don't forget to upvote.

1) At equilibrium. Y=AD = C+I+G+NX

=> Y = (400 + 0.8 YD) + 200 + (300 + 0.1 (Y* - Y)) + (-40)

=> Y = 860 + 0.8 (Y - TA + TR) + 0.1 (3000 - Y)

=> Y = 860 + 0.8 (Y - 0.25Y + 50) + 300 - 0.1Y

=> Y = 1160 + 0.8*0.75Y + 40 - 0.1Y

=> Y = 1200 + 0.5Y   

=> 0.5Y = 1200

=> Y = $2400

Therefore, Output gap = Y* - Y = $3000 - $2400 = $600

2) Again, Y = AD = C+I+G+NX

=> Y = (400 + 0.8 YD) + I₀ + (300 + 0.1 (Y* - Y)) + (-40)

=> Y = 1000 + I₀ + 0.5Y

=> 0.5Y = 1000 + I₀

Taking change on both sides:-

Since we need Y to reach Y*=$3000, Change required in Y = Output gap = $600

Therefore.  

Thus, investment needs to change by $300 in order to cover the output gap.

And, Budget surplus = TA - G - TR

When Y=$2400, BS = 0.25*2400 - (300+0.1*600) - 50 = 190 :Old Budget surplus

=> BS = 0.25Y - (300) - 50 {As output gap becomes zero, G = 300 + 0.1*0 = $300}

=> BS = 0.25*3000 - 350

=> BS = 400 :New Budget surplus

Thus, covering the output gap will lead to a rise in the budget surplus.

3) If G= G₀ (Constant level of govt spending) then we have the following changes in the equilibrium identity:-

Y = AD = C+I+G+NX

=> Y = (400 + 0.8 YD) + 200 + G₀ + (-40)

=> Y = 560 + 0.8 (Y - 0.25Y + 50) +G₀

=> Y = 600 + 0.6Y + G₀

=> 0.4Y = 600 + G₀

=>

=>

Therefore, expenditure multiplier increases from 2 previously to 2.5.

4) If TR = 50 + 100 = $150, Then:

Y = AD = C+I+G+NX

=> Y = (400 + 0.8 YD) + 200 + (300 + 0.1 (Y* - Y)) + (-40)

=> Y = 860 + 0.8 (Y - TA + TR) + 0.1 (3000 - Y)

=> Y = 1160 + 0.6Y + 0.8*150 -0.1Y

=> Y = 1280 + 0.5Y

=> 0.5Y = 1280

=> Y = $2560 :New level of output