Economic Equilibrium Modeling with GAMS

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26 PY0 = 1; $ONTEXT $MODEL:MRSCAL $COMMODITIES: PX ! PRICE INDEX FOR GOOD X PY ! PRICE INDEX FOR GOOD Y $CONSUMERS: RA ! REPRESENTATIVE AGENT $DEMAND:RA s:1 D:PX Q:1 P:PX0 D:PY Q:1 P:PY0 E:PX Q:X E:PY Q:Y $OFFTEXT $SYSINCLUDE mpsgeset MRSCAL $INCLUDE MRSCAL.GEN SOLVE MRSCAL USING MCP; * Compute the MRS using the solution values: MRS = PX.L / PY.L; * Display MRS <strong>with</strong> 8 decimals: OPTION MRS:8; DISPLAY MRS; The solution listing appears as follows: LOWER LEVEL UPPER MARGINAL ---- VAR PX . 0.400 +INF . ---- VAR PY . 1.600 +INF . ---- VAR RA . 2.000 +INF . PX PRICE INDEX FOR GOOD X PY PRICE INDEX FOR GOOD Y RA REPRESENTATIVE AGENT ---- 191 PARAMETER MRS = 0.25000000 COMPUTED MARGINAL
RATE OF SUBSTITUTION Demand Theory and MPSGE 27 Exercise (2.i): Show that the demand function is homothetic by uniform scaling of the X and Y endowments. The resulting MRS should remain unchanged. X = 20; Y = 20; $INCLUDE MRSCAL.GEN SOLVE MRSCAL USING MCP; * Compute the MRS using the new solution values: MRS = PX.L / PY.L; DISPLAY MRS; The solution to exercise (1.i): LOWER LEVEL UPPER MARGINAL ---- VAR PX . 0.400 +INF . ---- VAR PY . 1.600 +INF . ---- VAR RA . 40.000 +INF . ---- 255 PARAMETER MRS = 0.25000000 COMPUTED MARGINAL RATE OF SUBSTITUTION Exercise (2.ii): Modify the demand function calibration point so that the reference price of both X and Y equal unity. PX0 = 1; PY0 = 1; $INCLUDE MRSCAL.GEN SOLVE MRSCAL USING MCP; * Compute the MRS using solution values: MRS = PX.L / PY.L; DISPLAY MRS;
Page 1 and 2: Economic Equilibrium Modeling with
Page 3 and 4: Demand Theory and General Equilibri
Page 5 and 6: Demand Theory and MPSGE 3 who are i
Page 7 and 8: Figure 2. Indi erence Curves and Ut
Page 9 and 10: Y y = 1 Figure 5. A Calibrated Benc
Page 11 and 12: O:PX Q:1 I:PL Q:1 $PROD:Y O:PY Q:1
Page 13 and 14: For this model, the solution listin
Page 15 and 16: MRS = PX.L / PY.L; OPTION MRS:8; DI
Page 17 and 18: Demand Theory and MPSGE 15 Next, we
Page 19 and 20: Demand Theory and MPSGE 17 The key
Page 21 and 22: Demand Theory and MPSGE 19 In GAMS/
Page 23 and 24: Demand Theory and MPSGE 21 N.B. In
Page 25 and 26: PY0 = 1; LX0 = 1; $ONTEXT $MODEL:DE
Page 27: Demand Theory and MPSGE 25 ---- VAR
Page 31 and 32: $PROD:X $PROD:Y I:PLS Q:1 O:PX Q:1
Page 33 and 34: Demand Theory and MPSGE 31 ---- VAR
Page 37 and 38: $DEMAND:A s:SIGMA_A E:PX Q:XA E:PY
Page 43 and 44: Demand Theory and MPSGE 41 SC6 0.77
Page 45 and 46: MXA TRADE IN X FROM B TO A MXB TRAD
Page 47 and 48: Demand Theory and MPSGE 45 Suppress
Page 49 and 50: Applied General Equilibrium Modelin
Page 51 and 52: MPSGE Syntax 49 selected set of pap
Page 53 and 54: MPSGE Syntax 51 Final demand are de
Page 55 and 56: MPSGE Syntax 53 SAM displayed in Fi
Page 57 and 58: MPSGE Syntax 55 PARAMETER A(S) BENC
Page 59 and 60: * SECTION (ii) MPSGE MODEL DECLARAT
Page 61 and 62: MPSGE Syntax 59 is, the user cost o
Page 63 and 64: ---- VAR CD LOWER LEVEL UPPER MARGI
Page 65 and 66: LOOP(SC, * INSTALL TAX RATES FOR TH
Page 67 and 68: MPSGE Syntax 65 (ii) There are two
Page 69 and 70: INDEX 1 = HARBERGER UNIF_K UNIF_L U
Page 71 and 72: MPSGE Syntax 69 James R. Markusen a
Page 73 and 74: MPSGE Syntax 71 James R. Markusen a
Page 75 and 76: MPSGE Syntax 73 price (within the $
Page 77 and 78: MPSGE Syntax 75 X0(R) = SUM(G, YX0(
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7.6. Report Declaration MPSGE Synta
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MPSGE Syntax 79 FUNLOG triggers a f
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MPSGE Syntax 81 -------------------
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MPSGE Syntax 83 or to report percen
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MPSGE Syntax 85 Market Clearance fo
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MPSGE Syntax 87 Income Balance for
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CES Preferences and Technology A Pr
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CES Functions 91 calibrate function
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and compensated factor demands: Exe
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or, equivalently: X CES Functions 9
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CES Functions 97 $TITLE Two nonsepa
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* Now specify the two-level CES fun
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SCALAR DELTA /1.E-5/; SET FUNCTION
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CES Functions 103 $TITLE Numerical
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CES Functions 105 SCALAR SOLVED Fla
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CES Functions 107 $TITLE A Maquette
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$ONTEXT $MODEL:CHKCAL $COMMODITIES:
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PL.L = 1.0; CES Functions 111 * CHE
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Calibration: CES Functions 113 aij
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Calibration: CES Functions 115 ai 0
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118 1. Introduction GAMS (General A
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120 This MCP format encompasses a n
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122 That is: min P ij cijxij s.t. P
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124 PARAMETER ALPHA(I) Supply funct
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126 PARAMETER T(I,J) AD-VALOREM TAX
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128 , 2.t Aggregate world output eq
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130 POSITIVE VARIABLES E(R) FACTOR
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132 SET J PLAYERS /J1*J3/, I ACTION
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134 For these tests, both solvers a
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136 Consider the following nonlinea
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138 Associated Equation Type Variab
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Sequential Joint Maximization Relat
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Joint Maximization 143 maps prices
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Joint Maximization 145 Equilibrium
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OA Figure 1. Equilibrium in a 2x2 E
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If k =1or ( k ) < ( k,1 ), set k+1
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so that when 0 = 4, the (JM-D) prob
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Joint Maximization 153 Let (p; M) d
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Joint Maximization 155 which reduce
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Joint Maximization 157 Murtaugh, Br
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A.1. Two-by-Two Exchange Joint Maxi
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Joint Maximization 161 * The SJM pr
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); Joint Maximization 163 p(i) = -
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Joint Maximization 165 NP = (M+1) *
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SUM(C, ALPHA(C,H) * LOG(D(C,H)/DBAR
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OUTPUT.HOUSEOP 0.80 OUTPUT.CAPEOP 1
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Joint Maximization 171 VARIABLES Y(
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Joint Maximization 173 D.L(C,H) = (
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); Joint Maximization 175 LOOP(N, E
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Economic Equilibrium Modeling with GAMS

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