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### Deriving a contract curve in sage

Im trying to solve for the set of pareto efficent allocations using sage. So far i'm on the right track with my code of a two by two economy with consumer A and consumer B with resource constraints given by R1 and R2 for the total amount of good 1 and good 2.

xa1, xa2, xb1, xb2, a, b, R1, R2 = var('xa1, xa2, xb1, xb2, a, b')
Ua = xa1^a * xa2^b;
Ub = xb1^a*xb2^b;
R1=xa1+xb1;
R2=xb1+xb2;
MUa1=Ua.diff(xa1)
MUa2=Ua.diff(xa2)
MUb1=Ub.diff(xb1)
MUb2=Ub.diff(xb2)
MRSA=MUa1/MUa2
MRSB=MUb1/MUb2
solve([MRSA==MRSB],xa1)


The solution this code gives us is:

[xa1 == xa2*xb1/xb2]


I want to reduce xa1 to be a function of R1,R2 and xb1.

on paper this could be found by using the definitions of R1 and R2.

I've tried this before by including these variables in the square brackets of the solution but with no luck. Any help is appreciated.

### Deriving a contract curve in sage

Im trying to solve for the set of pareto efficent allocations using sage. So far i'm on the right track with my code of a two by two economy with consumer A and consumer B with resource constraints given by R1 and R2 for the total amount of good 1 and good 2.

xa1, xa2, xb1, xb2, a, b, R1, R2 = var('xa1, xa2, xb1, xb2, a, b')
b, R1, R2')
Ua = xa1^a * xa2^b;
Ub = xb1^a*xb2^b;
R1=xa1+xb1;
R2=xb1+xb2;
MUa1=Ua.diff(xa1)
MUa2=Ua.diff(xa2)
MUb1=Ub.diff(xb1)
MUb2=Ub.diff(xb2)
MRSA=MUa1/MUa2
MRSB=MUb1/MUb2
solve([MRSA==MRSB],xa1)


The solution this code gives us is:

[xa1 == xa2*xb1/xb2]


I want to reduce xa1 to be a function of R1,R2 and xb1.

on paper this could be found by using the definitions of R1 and R2.

I've tried this before by including these variables in the square brackets of the solution but with no luck. Any help is appreciated.

### Deriving a contract curve in sage

Im trying to solve for the set of pareto efficent allocations using sage. So far i'm on the right track with my code of a two by two economy with consumer A and consumer B with resource constraints given by R1 and R2 for the total amount of good 1 and good 2.

xa1, xa2, xb1, xb2, a, b, R1, R2 = var('xa1, xa2, xb1, xb2, a, b, R1, R2')
Ua = xa1^a * xa2^b;
Ub = xb1^a*xb2^b;
R1=xa1+xb1;
R2=xb1+xb2;
R2=xa2+xb2;
MUa1=Ua.diff(xa1)
MUa2=Ua.diff(xa2)
MUb1=Ub.diff(xb1)
MUb2=Ub.diff(xb2)
MRSA=MUa1/MUa2
MRSB=MUb1/MUb2
solve([MRSA==MRSB],xa1)


The solution this code gives us is:

[xa1 == xa2*xb1/xb2]


I want to reduce xa1 to be a function of R1,R2 and xb1.

on paper this could be found by using the definitions of R1 and R2.

I've tried this before by including these variables in the square brackets of the solution but with no luck. Any help is appreciated.