# Question:Evaluating and solving multi-equations

September 20 2013
Maple

1

I want to find the values of the following expressions, S, c3, c4,c5, cv, phi_3,phi_4,phi_5, c_3k,c_4k,c_5k,c_5b,G and B for given parameter values:  alpha,beta,g,k,b,sigma

(Note that cv is a function of c_3,c_4.c_5, so are the phi's and G)

1. S = (1-alpha)*((1-beta)*A*g*k^(g-1)-beta*(k+b)*A*(g-1)*g*k^(g-2))
2. c_3 = (1-alpha)*A*(1-g)*k^g
3. c_4 = (1-alpha)*(1-beta)*A*g*k^(g-1)
4. c_5 = -(1-alpha)*b*(A*g*k^(g-1)-1)
5. cv = c_3*sigma/(sqrt(1+c_4)*sqrt(c_3+c_5))
6. phi_3 = sigma/(sqrt(1+c_4)*sqrt(c_3+c_5))-(1/2)*cv/(c_3+c_5)
7. c_3k = -(1-alpha)*k*A*(g-1)*g*k^(g-2)
8. phi_4 = -(1/2)*cv/(1+c_4)
9. c_4k = (1-alpha)*(1-beta)*A*(g-1)*g*k^(g-2)
10. phi_5 = -(1/2)*cv/(c_3+c_5)
11. c_5k = -(1-alpha)*b*A*(g-1)*g*k^(g-2)
12. c_5b = (1-alpha)*(1-A*g*k^(g-1))
13. G = c_3k*phi_3+c_4k*phi_4+c_5k*phi_5
14. B = -(1+(1-alpha)*(beta*A*g*k^(g-1)-1))/(1-(1-alpha)*((1-beta)*A*g*k^(g-1)-beta*(k+b)*A*(g-1)*g*k^(g-2)))

If it helps consider the following parameter values, alpha=beta=g=0.3 , sigma=1, b=0.85, k=0.83

What is the most efficient way of doing this ? Can you please help me on this ? I will highly appreciate it !

Many thanks

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