Given the following system equations of price (P) and quantity (Q) determination in a widget market:

Demand: Q = 100 - 4P + 2G .....(1)

Supply:Q= 60 +10P - 3N......(2)

Where the price of substitute good, G = 10, and the cost of production N = 8.

1-a) by using therepeated substitution method only, please find equilibrium P and Q.

1-b) if G is up by 2, shows the impact of changing N on P and Q.

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+ .75Y........(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 usingthe matrix (linear) algebra only.

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

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

Show work for 2-a, 2-b, and 2-c by using the matrix (linear) algebra only using the repeated substitution method .

3. Consider the following system of equations:

10x₁+ x₂- 2x₃= 30

x₁- x₂+ 0x3= 1

3 x₁- 4X₂+x₃= 15.

_1,xto solve for the equilibrium values ofUse Cramer's rule