(50 points each)
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The following system of equations illustrates the algebraic form of a partial (individual) market equilibrium model, which is a model of price (P) and quantity (Q) determination simultaneously in a widget market:
Q = 120 – 20P…..(1)
Q = 40 + 20P……(2)
By using coefficients of endogenous variables (P and Q) matrix A, endogenous variables (P and Q) vector x, intercepts (constants) vector y, and Cramer’s rule, solve for the equilibrium values of P and Q.
(You must show the derivation of P and Q by using a matrix A, 2 vectors x and y, Ax = y, and the Cramer’s rule. This means that no credit for no work and no credit for using the repeated substitution method.)
Consider the simplified, two-equation, national income model
Y = C + I + G
C = a + b Y
Where national income (Y) and consumption (C) are endogenous variables and investment (I) and government spending (G) are exogenous variables.
The parameters in the consumption function, where a represent the autonomous consumption expenditure and b represents the marginal propensity to consume, respectively.
2-a) Set up this model with a 2 x 2 matrix of coefficients matrix, a 2 x 1 vector of endogenous variables, and a 2 x 1 vector of constants (consider I + G to be one constant).
2-b) The model can be expressed as Ax = y, where A is the coefficient matrix, x is the vector of endogenous variable, and y is the vector of constants. Find the solution of x.
(You must show your work. This means that no work = no credit.)
Business & Finance homework help