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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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