Question

Assume the following IS-LM model: Y = C + I + G C = .8(1-t)Y t =0.25 I = 900 - 50i G = 800 Md = 0.25Y -62.5i Ms =500.

(a)What will happen to the level of Y if G expands by 187.50? (b) What will happen to the composition of GDP? Explain and derive the numbers. (c). Was Investment crowded out? If so by how much.

Answer 1

Given, C= .8(1-t)Y, t =0.25, I = 900 -50i, G = 800, Md = 0.25Y- 62.5i, Ms = 500

IS: Y = C + I G

Y = .8(1-t)Y + 900 -50i + 800

= .8(1- 0.25) Y + 1700 - 50i

= .8(0.75)Y + 1700 -50i

=>Y - 0.6Y = 1700 - 50i

=> 0.4Y = 1700 - 50i

=> Y = 4250 - 125i

LM: Md = Ms

=> 0.25Y- 62.5i = 500

=> 0.25Y = 500 + 62.5i

=>Y = 2000 + 250i

Solving for the IS-LM model we get,

4250 - 125i = 2000 + 250i

=> 375i = 2250

=> i = 6

Y = 4250 - 125i = 4250 - 125(6) = 3500

(a) If G rises by 187.50, Y will also increase.

Y = C + I G +187.50

=> Y = .8(1-t)Y + 900 -50i + 800 + 187.50

=> Y = .8(1- 0.25) Y + 1887.50 - 50i

=> Y = .8(0.75)Y + 1887.50 - 50i

=>Y - 0.6Y = 1887.50 -50i

=> 0.4Y = 1887.50 -50i

=> Y = 4718.75 - 125i------> NEW IS CURVE

Solving for IS-LM, we get

4718.75 - 125i = 2000 + 250i

375i = 2718.75

=> i = 7.25

(b) GDP increases with increase in govt. expenditure.

Y = 4718.75 - 125i = 4718.75 - 125(7.25) = 3812.5

(c) Investment is crowded out by

I = 900 -50i = 900 - 50(7.25)= 537.5