[> restart; with(plots): with(LinearAlgebra):
[> F: =a[0]*K^a[1]*L^a[2];
[> a[0]: =2.248: a[1]: =0.404: a[2]: =0.803: F: =F;
[> plot3d([F], K=0..200, L=0..300);
[> AF_K: =F/K; AF_L: =F/L;
[> MF_K: =simplify(diff(F, K)): MF_L: =simplify(diff(F, L)):
Gradient_F: =[MF_K, MF_L];
[> G[1, 1]: =simplify(diff(MF_K, K)); G[1, 2]: =simplify(diff(MF_K, L));
G[2, 1]: =simplify(diff(MF_L, K)); G[2, 2]: =simplify(diff(MF_L, L));
[> Gesse: =Matrix(2, 2, [[G[1, 1], G[1, 2]], [G[2, 1], G[2, 2]]]):
Gessian: =simplify(Determinant(Gesse));
[> alpha[1]: =simplify(MF_K/AF_K); alpha[2]: =simplify(MF_L/AF_L);
alpha: =alpha[1]+alpha[2];
[> mu[1]: =simplify(MF_K/MF_L); mu[2]: =simplify(MF_L/MF_K);
/находим уравнения изоквант для ПФ/
[> Isokvanta_K_L: =solve(F=Q[0], K);
[> Q[0]: =10: implicitplot([F=Q[0], F=Q[0]+5, F=Q[0]+10, F=Q[0]+15, F=Q[0]+20], K=0..10, L=0..20, thickness=2);
/нахождение эластичности замены фактора фактором по формуле (8.2)/
[> H: =Matrix(3, 3, [[0, MF_K, MF_L], [MF_K, G[1, 1], G[1, 2]],
[MF_L, G[1, 2], G[2, 2]]]):
Det_H: =simplify(Determinant(H));
[> sigma: =simplify(((K*MF_K+L*MF_L)/(K*L))*(MF_K*MF_L/Det_H));
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