$TITLE: M2-5, Structure of a general-equilibrium model * simple (almost trivial) example of a one-good, one-factor, * one-consumer economy PARAMETERS LBAR labor supply (fixed and inelastic) ALPHA productivity parameter X = ALPHA*L; LBAR = 100; ALPHA = 2; NONNEGATIVE VARIABLES P price of X X quantity of X W wage rate INCOME income from labor supply; EQUATIONS ZPROFIT zeroprofits in X production CMKTCLEAR commodity (X) market clearing LMKTCLEAR labor market clearing CONSINCOME consumer income balance; ZPROFIT.. W/ALPHA =G= P; CMKTCLEAR.. X =G= INCOME/P; LMKTCLEAR.. LBAR =G= X/ALPHA; CONSINCOME.. INCOME =G= W*LBAR; MODEL GE /ZPROFIT.X, CMKTCLEAR.P, LMKTCLEAR.W, CONSINCOME.INCOME/; * set some starting values P.L = 1; W.L = 1; X.L = 200; INCOME.L = 100; * choose a numeraire W.FX = 1; OPTION MCP = PATH; SOLVE GE USING MCP; * double labor productivity ALPHA = 4; SOLVE GE USING MCP; * change numeraire W.UP = +INF; W.LO = 0; P.FX = 1; ALPHA = 2; SOLVE GE USING MCP; * double labor productivity ALPHA = 4; SOLVE GE USING MCP; $ontext formulated as an NLP the first theorem of welfare economics says that a competitive equilibrium is Pareto optimal in some very simple situation, such as with a single consumer this means that equilibrium can also be found as the solution to a simple NLP: maximizing utility subject to constraints. $offtext ALPHA = 2; LBAR = 100; VARIABLE U; EQUATIONS OBJECTIVE; OBJECTIVE.. U =E= X**0.5; MODEL GE_NLP / OBJECTIVE, ZPROFIT, CMKTCLEAR, LMKTCLEAR, CONSINCOME/; SOLVE GE_NLP USING NLP MAXIMIZING U;