Trying to solve a demand-supply equilibrium here and them find a partial derivative of the equilibrium with respect to the parameters.
S[q_] := -Log[q] d[Il_, beta_] := phi*v*zeta/(1 - beta - delta)*(A/(v*zeta*(1 + phi*Il)))^(v/(v - 1)) S1[Il_, beta_, ig_] := S[(delta + beta)*i - beta*ig - (1 - beta - delta)*Il]
d is the demand and
S1 is the supply. The equilibrium price is expressed in terms of the parameters
f[beta_, ig_] := x /. Solve[d[x, beta] == S1[x, beta, ig], x, Reals][]
Now I want to look at the partial derivative of the equilibrium wrt
ig as a function of beta.
Eff[beta_] := D[f[beta, ig], ig] /. ig -> 0.03
Eff() at any value is taking forever to compute. The function
f() is well-defined and is giving me quick output when I plug in some arguments.
Is there anything wrong in the code or is it just computationally time-consuming?
Values of the symbols are as follows.
phi = 0.2 v = 1.5 zeta = 1 delta = 0.04 A = 1 i = 0.05