Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Economics 214 Lecture 13 Systems of Equations Examples of System of Equations Demand and Supply IS-LM Aggregate Demand and Supply Demand and Supply Demand : q d P I P S Supply : q s P W Equilibriu m : q d q s q q quantity P price P S price substitute good I income W wage rate IS-LM IS : ln( i ) ln( Y ) ln( G ) LM : ln( i ) ln( Y ) ln( M / P) i interest rate Y real GDP G real gov' t spending P price level Solving System of Equations Repeated Substitution Matrix Algebra or linear Algebra Solving System of Equations Economic Models typically consist of a number of equations that represent identities, behavioral relationships, and conditions that constitute an equilibrium. These equations include both variables, which are economic quantities and parameters, which are unvarying constants. Solving Systems of Equations Variables in a system are exogenous if determined outside the system or endogenous if the are determined within the system. A solution to the model is a representation of the endogenous variables as functions of only the parameters of the model and the exogenous variables. Solving our Demand and Supply model Using the equilibriu m condition that q d q s q, we can rewrite our demand and supply equations as demand : q P I P S supply : q P W Setting the two equal, we get P W P I P S P ( ) I P S W or or S P I P W Solving our Demand & Supply Model To find the equilibriu m quantity, we will substitute our solution for price into the supply equation. S q I P W W S I P W S I P W Solving our IS-LM Model IS : ln( i ) ln( Y ) ln( G ) LM : ln( i ) ln( Y ) ln( M / P ) In equilibriu m, the interest rate in both equations is equal. We will therefore set both equations equal and solve for equilbrium ln( Y ). ln( Y ) ln( M / P) ln( Y ) ln( G ) ln( Y ) ln( G ) ln( M / P) or ln( Y ) ln( G ) ln( M / P ) Solving our IS-LM Model We can get the equilibriu m interest rate, by substituti ng our solution for the equilibriu m income into either the IS or the LM equation. ln( i ) ln( G ) ln( M / P ) ln( M / P ) ln( G ) ln( M / P ) ln( G ) ln( M / P )