How to express endogenous variables in terms of exogenous variables?

Question

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?

Answer 1

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))}