1 | initial version |

With a little bit of playing with the code I found that the best way to solve this problem analytically is by specifying prices and income in the `var()`

command. the code I've used is:

x, y, l, p, q, R= var('x, y, l, p, q, R')
U = x^7/10 * y^3/10; U
m = p*x+q*y; m
solve(m == R, y)
L = U - l * (m - R); L
dLdx = L.diff(x); dLdx
dLdy = L.diff(y); dLdy
dLdl = L.diff(l); dLdl
solve([dLdx == 0, dLdy == 0, dLdl == 0], x, y, l)

2 | No.2 Revision |

With a little bit of playing with the code I found that the best way to solve this problem analytically is by specifying prices and income in the `var()`

command. the code I've used is:

```
x, y, l, p, q, R= var('x, y, l, p, q, R')
U = x^7/10 * y^3/10; U
m =
```~~p~~*x+q*y; p*x+q*y; m
solve(m == R, y)
L = U - l * (m - R); L
dLdx = L.diff(x); dLdx
dLdy = L.diff(y); dLdy
dLdl = L.diff(l); dLdl
solve([dLdx == 0, dLdy == 0, dLdl == 0], x, y, ~~l)~~l)
[[x == 7/10*R/p, y == 3/10*R/q, l == 22235661/100000000000*R^9/(p^7*q^3)], [x == 0, y == R/q, l == 0], [x == R/p, y == 0, l == 0]]

Where p,q and R are the prices of good x and good y and an arbitrary income level.

Very useful!

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