Economic Equilibrium Modeling with GAMS

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14 PLS ! CONSUMER VALUE OF LEISURE $CONSUMERS: RA ! REPRESENTATIVE AGENT $PROD:LS O:PL Q:PHI I:PLS Q:1 $PROD:X $PROD:Y O:PX Q:1 I:PL Q:CX O:PY Q:1 I:PL Q:CY $DEMAND:RA s:1 E:PLS Q:120 D:PLS Q:1 P:1 D:PX Q:1 P:1 D:PY Q:1 P:1 $OFFTEXT $SYSINCLUDE mpsgeset LSUPPLY $INCLUDE LSUPPLY.GEN SOLVE LSUPPLY USING MCP; We can use this model to evaluate the wage elasticity of labor supply. In the initial equilibrium (computed in the last statement) the demands for x, y and L all equal 40. A subsequent assignment toPHI (below) increases labor productivity. After computing a new equilibrium, we can use the change in labor supply to determine the wage elasticity of labor supply, an important parameter in labor market studies. It should be emphasized that the elasticity of labor supply should be an input rather than an output of a general equilibrium model { this is a parameter for which econometric estimates can be obtained. Here is how the programming works. First, we declare some scalar parameters which we will use for reporting, then save the \benchmark" labor supply in LS0: SCALAR LS0 REFERENCE LEVEL OF LABOR SUPPLY ELS ELASTICITY OF LABOR SUPPLY WRT REAL WAGE; LS0 = LS.L;
Demand Theory and MPSGE 15 Next, we modify the value of scalar PHI, increasing labor productivity by 1%. Because this is a neoclassical model, this change is equivalent to increasing the real wage by 1%. We need to recompute equilibrium prices after having changed the PHI value: PHI = 1.01; $INCLUDE LSUPPLY.GEN SOLVE LSUPPLY USING MCP; We use this solution to compute and report the elasticity of labor supply as the percentage change in the LS activity: ELS = 100 * (LS.L - LS0) / LS0; DISPLAY ELS; As the model is currently constructed, the wage elasticity oflabor supply equals zero. This is because the utility function is Cobb-Douglas over goods and leisure, and the consumer's only source of income is labor. As the real wage rises, this increases both the demand for goods (labor supply) and the demand for leisure. These e ect exactly balance out and the supply of labor is unchanged. (a) One way in which the labor supply elasticity might di er from zero in a model with Cobb-Douglas nal demand is if there were income from some other source. Let the consumer be endowed with good x in addition to labor. What x endowment is consistent with a labor supply elasticity equal to 0.15? Hint: Let be the uncompensated labor supply elasticity. Algebraic derivation leads to the following formula: where: ` is the value share of leisure, Px is the price of X, EX is the endowment of commodity X, PL is the price of labor, L is the endowment oflabor. =( `PxEX)=(PLL(1 , `) , `PxEX) (b) A second way to calibrate the labor supply elasticityistochange the utility function. We can do this bychanging the s:1 to s:SIGMA,whereSIGMA is a scalar value representing the benchmark elasticity of substitution between x, y and L in nal demand. Modify the program to include SIGMA as a scalar, and nd the value for SIGMA consistent with a labor supply elasticity equal to 0.15. Hint: Let be the uncompensated labor supply elasticity. The algebraic derivation of using a CES utility function, leads to the following formula: where: = LEIS LSUP ( , 1)(1 , `)
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: MRS = PX.L / PY.L; OPTION MRS:8; DI
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 and 28: Demand Theory and MPSGE 25 ---- VAR
Page 29 and 30: RATE OF SUBSTITUTION Demand Theory
Page 31 and 32: $PROD:X $PROD:Y I:PLS Q:1 O:PX Q:1
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
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MPSGE Syntax 65 (ii) There are two
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INDEX 1 = HARBERGER UNIF_K UNIF_L U
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MPSGE Syntax 69 James R. Markusen a
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MPSGE Syntax 71 James R. Markusen a
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MPSGE Syntax 73 price (within the $
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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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