clear all
set more off
version 11.1
clear all
set mem 500m
global points=2500
set obs $points

// parameters
global alpha=.3   // cobb douglas function parameter : (x^alpha)*(y^(1-alpha))
global budget=100
global p1=2
global p2=3

//calculations

gen counter=_n
gen y=(($budget/$p2)/$points)*counter
gen x=($budget -$p2*y)/$p1

scalar x_sol=($budget*$alpha)/$p1
di x_sol
global sol1=x_sol
scalar y_sol=($budget-$p1*x_sol)/$p2
di y_sol
global sol2=y_sol
scalar utility=(x_sol^$alpha)*(y_sol^(1-$alpha))
di utility
gen ux=x if (x>0.1*($budget/$p1))&(x<0.9*($budget/$p1))   // sum to find solution point
gen uy= (utility^(1/(1-$alpha)))/(ux^($alpha/(1-$alpha)))
 
 
 twoway line y x || line uy ux    ||,  ytitle( "Cooperation") xtitle( "Conflict" )title( "Cobb-Douglas Utility Function, alpha = $alpha ",span  ) subtitle("Equilibrium: Conflict=$sol1, Cooperation= $sol2")	legend( label(1 "Budget Constraint") label(2 "Utility Function") )  note("Model Parameters: Budget=$budget, p1=$p1, p2=$p2")

//format solution