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Transform the following systems of linear equations into matrix forms. a. General equilibrium model: 2 goods QD₁ = 30-P₁-P2; Qs₁ = 2p₁ - 5 QD2 = 23+ P₁-P2; Qs2 = P2 - 3

Transform the following systems of linear equations into matrix forms. a. General equilibrium model: 2 goods QD₁ = 30-P₁-P2; Qs₁ = 2p₁ - 5 QD2 = 23+ P₁-P2; Qs2 = P2 - 3

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 23EQ: 23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes...
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Transform the following systems of linear equations into matrix forms. a. General equilibrium model: 2 goods Qo1 = 30 -P1 -Pz; Osı = 2p1 – 5 Qp2 = 23 +P1 -P2; Qs2 =P2 - 3 %3D b. IS-LM model: Closed economy i. Aggregate expenditure: AE = C +1 + G Note: Exogenous government expenditure: G = Go ii. Consumption function: C = a + c(1 - t)Y, where a > 0, and 0 < c,t <1 Note: C is consumption and Y is disposable income. a, c, and t are constants. c is the marginal propensity to consume and t is the tax rate. Hence, c and t are parameters. i. Investment function: I = d – ei, where d,e > 0, and 0 <i<1 Note: / is investment spending and i is interest rates. d and e are constants. iv. Money market: Money demand function: Mp = kY – li Exogenous money supply: Ms = Mo At equilibrium: Mp = Ms where k,l> 0, and 0 < i <1 Note: Y is disposable income and i is interest rates. Money supply is exogenous, assuming that the central bank determines its level. Hint: The variables in the matrix (i.e., at the equilibrium) are: Y*, C',I', and i". The coefficient matrix will be 4 x 4.
Transcribed Image Text:Transform the following systems of linear equations into matrix forms. a. General equilibrium model: 2 goods Qo1 = 30 -P1 -Pz; Osı = 2p1 – 5 Qp2 = 23 +P1 -P2; Qs2 =P2 - 3 %3D b. IS-LM model: Closed economy i. Aggregate expenditure: AE = C +1 + G Note: Exogenous government expenditure: G = Go ii. Consumption function: C = a + c(1 - t)Y, where a > 0, and 0 < c,t <1 Note: C is consumption and Y is disposable income. a, c, and t are constants. c is the marginal propensity to consume and t is the tax rate. Hence, c and t are parameters. i. Investment function: I = d – ei, where d,e > 0, and 0 <i<1 Note: / is investment spending and i is interest rates. d and e are constants. iv. Money market: Money demand function: Mp = kY – li Exogenous money supply: Ms = Mo At equilibrium: Mp = Ms where k,l> 0, and 0 < i <1 Note: Y is disposable income and i is interest rates. Money supply is exogenous, assuming that the central bank determines its level. Hint: The variables in the matrix (i.e., at the equilibrium) are: Y*, C',I', and i". The coefficient matrix will be 4 x 4.
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