# How to express endogenous variables in terms of exogenous variables?

I have 11 endogenous variables (RD, NR, WR, Q, NQ, R, L, W, NU, C1, C2) and two exogenous variables (EE, K).

I'm trying to find $RD = f(EE, K),\, NR = f(EE, K),\, ...,\, C2 = f(EE, K)$.

Hence, I tried the following code:

{e, α, σ, δ, β1, β2, β3, a, ε, η, q, θ, ω} =
{1.1, 0.66, 0.7, 0.04, 0.6, 0.02, 0.38, 0.1, 1, 0.55, 1.01, 7.7, 0.7}

Eliminate[{
RD == (e NR)^α,
α e^α NR^(α - 1) == WR/(EE q),
WR == θ EE^a,
Q == (β1 NQ^((σ - 1)/σ) + β2 R^((σ - 1)/σ) + β3 k^((σ - 1)/σ))^(σ/(σ - 1)),
β1 (Q/NQ)^(1/σ) == W,
β2 (Q/R)^(1/σ) == EE q,
NR + NQ + NU == 1 - L,
W (NR + NU) == WR NR,
(a/(1 - a)) (C1/C2) == EE,
L == (a^a (1 - a)^(1 - a) EE^-a W)^- ε,
ω Q EE^η - EE C2 -EE q (R - RD) == 0},
{RD, NR, WR, Q, NQ, R, L, W, NU, C1, C2}]


Also, I tried Solve[{above 11 eqations}, {EE,K}] and Reduce, and still it does not work.

Could anyone give me some hints?

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Oh…you're still working on this set of equations? (Related question: mathematica.stackexchange.com/questions/11947/…) – xzczd Dec 22 '12 at 6:41
Yes. Thanks for everyone's help. That linked problem already solved. This equation is based on that question. Do you kindly give me some suggestions if possible? – David Dec 22 '12 at 6:51

Not an answer. You could "solve" manually the easy ones and work numerically on the rest :

{e, α, σ, δ, β1, β2, β3, a, ε, η, q, θ, ω} =
Rationalize@{1.1, 0.66, 0.7, 0.04, 0.6, 0.02, 0.38, 0.1, 1, 0.55, 1.01, 7.7, 0.7};

equations //.
{WR -> \[Theta] EE^a,
C1 -> 9 C2 EE,
NR -> (1009899 (3333/7)^(16/17) EE^(45/17))/(61250000000 2^(14/17) 5^(13/17)),
RD -> (3333 (3333/7)^(16/17) (EE^(45/17))^(33/50))/(17500000 2^(14/17) 5^(13/17))}

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Since David asked for hints, I think this is a legitimate answer. – m_goldberg Dec 23 '12 at 0:28