Due date: at the beginning of the class on Wednesday, 11/28/2012 (50 points each) 1. Microeconomics: 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 Cramers 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 Cramers rule. This means that no credit for no work and no credit for using the repeated substitution method.) 2. Macroeconomics: 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.)
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