Demand Curve by EQ0v8QPm


									This workbook solves the standard consumer theory problem with Excel's Solver.
             max U = XaYb
             s.t. M = PxX + PyY

Via calculus, you set up the Lagrangean and solve for X* and Y* as functions of a, b, Px, Py, and M.

X* as a function of Px, ceteris paribus , is the individual demand curve for X.

From the ConsumerTheoryProblem sheet, use the CS Wiz add-in to do a comparative statics analysis that derives the demand curve.

The results of such an analysis are displayed in the DemandCurve sheet.
s that derives the demand curve.
Objective function                                     Execute Tools: Solver to get the initial solution.
                             a b
max U                   0 U=X Y
                                                       Run the Comparative Statics Wizard to get a demand curve.
                                                       The shock variable is Px (cell B11); vary it by 0.1 with 5 shocks.
Endogenous Variables
X                       0 units of X
Y                       0 units of Y

Exogenous Variables
Px                     2 $/unit
Py                     6 $/unit
M                   144 $
a                    0.5
b                    0.5

Budget               144 M = PxX + PyY
                         Excel can handle an inequality constraint, but let's keep it simple.
 et a demand curve.
by 0.1 with 5 shocks.
Comparative Statics Analysis
The following exogenous variables comprised the INITIAL problem:
s Variable Value
Px                  2
Py                  6
M                144
a                 0.5
b                 0.5

                         Optimal  Optimal
Exogenou Optimal        Endogeno Endogeno
 s Shock Objective         us       us
 Variable Function       Variable Variable
           Obj Fn (or
           Eq Cond)
    Px      ($B$2)         X         Y
         2 20.78461           36       12
       2.1 20.2837      34.28572       12
       2.2 19.81735     32.72727       12
       2.3 19.38175     31.30435       12
       2.4 18.97367           30       12
       2.5 18.59032     28.79913 12.00036

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