1.By using the repeated substitution method,

Solving the following system of equations, which is a model of price and quantity determination in a one-good, widget, market:

Q_d= 100- 10P + 2G.....(1)

Q_s= 60 +20P - 3N..........(2)

Q = Q_d=Q_{s..................... ..(3)}

G= 11 ..............................(4)

N= 6 ................................(5)

(i)Find the equilibrium values of P andQ.

(ii)If G is up by 2 and other things are equal, What will be the new P and Q.

(iii)If N is up by 2 and other things are equal, What will be the new P and Q.

2. Consider the simplified national income model:

AD = C + I............(1)

Where AD is aggregate demand, C is consumption, and I is investment. Consumption is determined by a behavioral equation, which in this problem takes the form

C= 3,300+ .8Y........(2)

Y is national income.

Y and C are ENDOGENOUS VARIABLE and Investment is exogenous VARIABLE. initially we assume

I =1,500...................(3)

The equilibrium condition requires that aggregate demand equals national income, that is,

AD = Y..................(4)

By using the matrix (Linear) algebra, not by using repeated substitution method, do

i)Determine the equilibrium level of national income (Y) and consumption (C.)

ii)Show the overall change or the comparative statics of I increased by 500 on Y and C.

3.Consider the following system of equations:

3x₁+ 2x₂- 2x₃= -15

4x₁+ 3x₂+3x₃= 17

2x₁-x₂-x₃= -1

Use Cramer's rule to solve for the equilibrium values of x_1,x_{2, and}x₃in the system of equations.

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

Demand: Q = a - b P + e G .....(1)

Supply:Q= c +d P - f N......(2)

Where the price of substitute good, G, and the cost of production, N, are the exogenous variables. Q and P are endogenous variables.

By using theMATRICES and VECTORS method (MATRIX ALGEBRA), please find equilibrium P and Q.

please show work i need to understand this.

5. Ch. 4

By using REPEATED SUBSTITUTION method only, please answer the followingMacroeconomics question:

Consider the simplified, two-equation, national income model

Y = C + I

C=a+b Y

Where national income (Y) and consumption (C) are endogenous variables and investment (I) are exogenous variables.

The parameters in the consumption function, wherearepresent the autonomous consumption expenditure and b represents the marginal propensity to consume, respectively.