Question

2. Consider the simplified national income model:

    Y = C + I…………(1)

                          

Where Y is national income, C is consumption, and I is investment. Consumption is determined by a behavioral equation, which in this problem takes the form

     C= 3000+ .75 Y……..(2)

Where Y and C are endogenous variables and Investment is exogenous, and, initially we assume

I =1000……………….(3)

(2-a) Determine the equilibrium level of national income (Y) and consumption (C) by using the matrix (linear) algebra only.

(2-b) Determine the overall change (comparative statics analysis) of the equilibrium level of national income (Y) and consumption

(2-c) if new I = 600, decreased by 400.

Show Work. Linear Algebra Only!

Answer 1

Here,

Y = C + I

C = 3000 + .75Y

I = 1000

Let us put the a in place of 3000(absolute consumption)

b in place of .75

Now we have

Y = C + I

C = a + bY

We can also write these equations as

Y - C = I

C - bY = a

Putting them in matrix form as

By solving it with Cramer's rule we get

Now putting the values of a,b,I we get

Y = 3000+1000/1-.75 ......(I)

= 16000.

C = 3000+.75×1000/1-.75 ......(ii)

= 15000

This is the equilibrium level of income and consumption.

If I is reduced to 600 let's see the change in equilibrium level of Income and consunconsu by putting 600 in place 1000 in the above given equation (I) and (ii) we get

Y = 3000+ 600/ 1-.75

= 14,400

C = 3000 + 600×.75/ 1-.75

= 13,800

Now we can compare the two equilibrium level and say that as investment was reduced by 400 income went down to 1600

Whereas , consumption went down to 1200

Thus less investment resulted in lesser income and consumption level of the economy.