#To read the text above and translate it as a lamda function from sympy import Symbol c = Symbol("c") t = Symbol("t") from sympy.parsing.sympy_parser import parse_expr U1_e = parse_expr(U1) U2_e = parse_expr(U2) from sympy.utilities.lambdify import lambdify U1_l = lambdify((c,t),U1_e) U2_l = lambdify((c,t),U2_e) #to realy draw the EdgeworthBox draw_Ed_Bow(U1_l,U2_l,8,6,colors=["k","Orange", "lightblue","mistyrose"],Num_ind=5) draw_Ed_Bow(U1_l,U2_l,8,6,Xlab="Courgettes",Ylab="Tomatoes",AlPoint=(3,3),Contract_draw=False) plt.show()

#The main function def draw_Ed_Bow(U1,U2, Xmax, Ymax, Xmin=10**(-6), Ymin=10**(-6), Utility_Show = False, Num_ind = 10,Xlab ="X",Ylab="Y",e=200, Contract_draw=True,AlPoint = None,colors =["black","Orange", "blue","red"],Utility_draw = True): """ Input : U1: Utility of the 1st agent (must depend on 2 variables) U2: Utility of the 2nd agent (must depend on 2 variables) Xmax : the limit of the box Ymax: the limit of the box Xmin=10**(-6): the limit of the box (default: set to ~0 to avoid problems with log expressions) Ymin=10**(-6): the box limit (default: set to ~0 to avoid problems with log expressions) Utility_Show = False: Show utility levels on the Edgeworth box Num_ind = 10 : Number of indifference curves per agent e = 200 : Number of steps to compute the utility levels and the contract curve Contract_draw = True: Draw the contract curve AlPoint = None : show an allocation point and his 2 indifference curves. Should be a tuple/list (x,y) colors = ["black","Orange", "blue","red"] : To choose the color of : [ContractCurve, endowment point, indifference curves Agent1, indifference curves agent2] Utility_draw = True : Draw the indefrence curves Output: None (but draws the Edgeworth box) """ delta = min((Xmax-Xmin)/e,(Ymax-Ymin)/e) x = np.arange(Xmin, Xmax, delta) #Tomates y = np.arange(Ymin, Ymax, delta) #courgettes X, Y = np.meshgrid(x, y) Z1 = lambda x,y : U1(x,y) Z2 = lambda x,y : U2(Xmax-x,Ymax-y) #the contract curve Num_ind_1 = Num_ind Num_ind_2 = Num_ind if Contract_draw == True: Z2grad = np.gradient(Z2(X,Y)) Z1grad = np.gradient(Z1(X,Y)) out = (Z2grad[0]*Z1grad[1]-Z2grad[1]*Z1grad[0]) Cont = plt.contour(X,Y,out,colors=colors[0],levels=[0]) fmt = {} strs = ["Contract curve"] for l, s in zip(Cont.levels, strs): fmt[l] = s plt.clabel(Cont, Cont.levels, inline = True, fmt = fmt, fontsize = 10) C_curv = abs(pd.DataFrame(out ,index=y, columns=x)) C_curv = C_curv.index @ (C_curv == C_curv.apply(min)) xC_curv = np.arange(Xmin,Xmax,(Xmax-Xmin)/(Num_ind+1)) C_curv = np.interp(xC_curv,C_curv.index,C_curv) Num_ind_1 = pd.Series(Z1(xC_curv,C_curv)).sort_values(ascending=True) Num_ind_2 = pd.Series(Z2(xC_curv,C_curv)).sort_values(ascending=True) #Draw the dotation point and his curves if AlPoint != None: plt.scatter(AlPoint[0],AlPoint[1],s=200,marker=".",color = colors[1],label="Allocation point") Num_ind_1 = [Z1(AlPoint[0],AlPoint[1])] Num_ind_2 = [Z2(AlPoint[0],AlPoint[1])] #draw the indifference curve if Utility_draw == True: C1 = plt.contour(X, Y, Z1(X,Y),colors = colors[2],levels=Num_ind_1) C2 = plt.contour(X, Y, Z2(X,Y),colors = colors[3],levels=Num_ind_2) if Utility_Show == True: fmt = {} strs = round(pd.Series(C1.levels[:]),1) for l, s in zip(C1.levels, strs): fmt[l] = s plt.clabel(C1, C1.levels, inline = True, fmt = fmt, fontsize = 10) #Utility level2 fmt = {} strs = round(pd.Series(C2.levels[:]),1) for l, s in zip(C2.levels, strs): fmt[l] = s plt.clabel(C2, C2.levels, inline = True, fmt = fmt, fontsize = 10) plt.title("Edgeworth box") plt.xlabel(Xlab) plt.ylabel(Ylab)

# Utility of 1st agent (depend on X,Y): U1 = lambda x, y: np.log10(x) + y ** (0.5) + 10 # Utility of 2nd agent (depend on X,Y): U2 = lambda x, y: 0.6 * np.log10(x) + 2 * (y) ** 0.2 draw_Ed_Bow(U1, U2, 4, 8, e=300,Num_ind=8,Contract_draw=False) plt.show()

# Utility of 1st agent (depend on X,Y): U1 = lambda x, y: np.log10(x) + y ** (0.5) + 10 # Utility of 2nd agent (depend on X,Y): U2 = lambda x, y: 0.6 * np.log10(x) + 2 * (y) ** 0.2 draw_Ed_Bow(U1, U2, 4, 8, e=300,Num_ind=3) plt.show()

#Utility of 1st agent (depend on X,Y): U1 = lambda b,f : 2*b + f #Utility of 2nd agent (depend on X,Y): U2 = lambda b,f : 12*b + (10-f)*f draw_Ed_Bow(U1,U2,8,4,Num_ind=4,colors=["k","Orange", "lightblue","mistyrose"]) draw_Ed_Bow(U1,U2,8,4,Xlab="Book",Ylab="Food",AlPoint=(3,0.5),Contract_draw=False) plt.show()

#Utility of 1st agent (depend on X,Y): U1 = lambda c,t : c**0.5 * t**0.3 #Utility of 2nd agent (depend on X,Y): U2 = lambda c,t : c**0.5 * t**0.5 draw_Ed_Bow(U1,U2,8,6,colors=["k","Orange", "lightblue","mistyrose"],Num_ind=5) draw_Ed_Bow(U1,U2,8,6,Xlab="Courgettes",Ylab="Tomatoes",AlPoint=(3,3),Contract_draw=False) plt.show()

#Utility of 1st agent (depend on X,Y): U1 = lambda c,t : 2*c + t #Utility of 2nd agent (depend on X,Y): U2 = lambda c,t : 12*c +(10-t)*t draw_Ed_Bow(U1,U2,8,4,colors=["k","Orange", "lightblue","mistyrose"],Num_ind=5) draw_Ed_Bow(U1,U2,8,4,Xlab="Courgettes",Ylab="Tomatoes",AlPoint=(2,2),Contract_draw=True) plt.show()

#Utility of 1st agent (depend on X,Y): U1 = lambda x,y : x*np.exp(-(x**2 + y**2)) #Utility of 2nd agent (depend on X,Y): U2 = lambda c,t : c**0.5 * t**0.5 maxval = 2.5 draw_Ed_Bow(U1,U2,maxval,maxval,Ymin=0,Xmin=0,Contract_draw=False,e=600,Num_ind=10) draw_Ed_Bow(U1,U2,maxval,maxval,Ymin=0,Xmin=0,Contract_draw=True,e=600,Num_ind=10,Utility_draw = False) plt.title("Not an Edgeworth Box !") plt.show()

#Utility of 1st agent (depends on X,Y): UM = lambda x,y : (-1 + (x+6)**2 + (x+6) * (y*4) )/((x+6) + (y*4))+100 #Utility of 2nd agent (depends on X,Y): UH = lambda x,y : (-1 + x**2 + x * y )/(x + y)+100 draw_Ed_Bow(UH,UM,8,4,Xlab="Courgettes",Ylab="Tomatoes",Num_ind=5) plt.text(-0.3,-0.2,"M") plt.text(8.1,4.1,"H") plt.show()

#Utility of 1st agent (depends on X,Y): UM = lambda x,y : (-1 + (x+6)**2 + (x+6) * (y*4) )/((x+6) + (y*4))+100 #Utility of 2nd agent (depends on X,Y): UH = lambda x,y : (-1 + x**2 + x * y )/(x + y) +100 draw_Ed_Bow(UH,UM,8,4,Xlab="Courgettes",Ylab="Tomatoes",Num_ind=5) plt.text(-0.3,-0.2,"M") plt.text(8.1,4.1,"H") plt.show()