Economic Equilibrium Modeling with GAMS

32
SUPPLY WRT REAL WAGE
Exercise (3.ii) Alternatively, change the utiliy function. Let us change s:1 to s:SIGMA,
where SIGMA is a scalar value representing the benchmark elasticity of subsitution between
X, Y and L in nal demand. Find the value for SIGMA consistent with a labor supply
elasticity of 0.15
Solving for in the expression for given in the hint, we have that:
= LSUP
LEIS
1
+1
1 , `
To compute in this exercise we are given: =0:15, ` =1=3, change in PHI from
1.0 to 1.01, thus with =0:15 we have LSUP =80:12 and LEIS =39:88.
* Compute SIGMA:
SCALAR LSUP Labor supply /80.12/
LEIS Demand for leisure /39.88/;
* Value of SIGMA consistent with ELS = 0.15:
SIGMA = ETA * (LSUP/LEIS) * (1/(1-Shl)) + 1;
DISPLAY SIGMA;
* Return to the benchmark value of the endowment of X and labor prod:
EX0 = 0;
PHI = 1;
$INCLUDE LSUPPLY.GEN
SOLVE LSUPPLY USING MCP;
Listing output:
---- 679 PARAMETER SIGMA = 1.452 ELASTICITY OF
SUBSTITUTION IN
CONSUMPTION
LOWER LEVEL UPPER MARGINAL
---- VAR X . 40.000 +INF .
---- VAR Y . 40.000 +INF .
---- VAR LS . 80.000 +INF .
---- VAR PX . 1.000 +INF .
---- VAR PY . 1.000 +INF .
---- VAR PL . 1.000 +INF .