Hi there,

I work with a standard NK model including final and intermediate firms. Intermediate firms face monopolistic competition. There is investment as well as consumption. I have implemented habit persistence preferences in consumption and capital adjustment costs.

In this model, marginal costs in steady-state are equal the inverse mark-up (markup > 1), therefore, they are smaller than 1. **This means that labor effort is paid lower than the additional value of output it produces (wedge).** Because households own the intermediate firm (which pays less wage than under no mark-up), there must be dividend payments for the household.

How I solve for the steady-state: I solve for labor market equilibrium (I isolate steady-state consumption depending only on output) and then I solve for capital market equilibrium (I isolate steady-state investment depending only on output). Then I take the resource constraint, plug in consumption and investment and solve for steady-state output. The rest is straightforward.

I’m unable to find the steady-state. I don’t know how to deal with gains because they enter the household’s budget constraint exogenously. I would expect the household not incorporating lower wage payments as he owns the firm and gets dividends instead. But actually, he does, in terms of marginal cost-depending steady-state wage payments.

At the end, I don’t know how to correct the wedge between actually produced output and the corresponding too low wage payments (which should not be incorporated… …).

Should I introduce steady-state fix costs? How does it work? Or fixing labor effort in steady- state? Any consequences?

```
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Here are some steady-state equations:
b_habit = 0.87; % Habit persistence in consumption
xi = 0.23; % Capital adjustment costs parameter
alpha = 0.20; % Share of capital in technology
beta = 0.997; % Discount factor
delta = 0.025; % Depreciation of capital
sigmaC = 2; % Risk aversion in individual's consumption
sigmaL = 1.5; % Labor disutility
theta_p = 0.65; % Proportion of price setting constrained firms
rho_r = 0.8; % Monetary policy parameter
phi_r = 2; % Monetary policy parameter for inflation weight
mu = 1.1; % Mark-up on intermediate goods
psi = 1.5; % Substitutability between intermediate goods
rho_a = 0.95; % Productivity coefficient
chi_X = 1; % Labor disutility parameter
Infl_x_H = 1;
Infl_H = 1;
price_dispersion_h = 1;
A_h = 0;
q_h = 1;
mc_h = (1/mu);
r_h = 1/beta;
a_3 = (1/xi);
a_1 = ((delta)^(a_3));
a_2 = (delta - ((delta)/(1-a_3)));
z_h = (1/beta) - (1-delta) - (((a_1)/(1-a_3))*(delta^(1-a_3))) - a_2 + a_1*((delta)^(1-a_3)) ; % real remuneration of capital
w_h = (1-alpha)* ((mc_h)^(1/(1-alpha))) * ( ( alpha/z_h )^(alpha/(1-alpha)) ) ; % real wage
y_h = ( ( (1-b_habit)*( (1-delta*alpha*(1/z_h))/ ( ((chi_X/w_h)*((1-alpha)^(sigmaL))*((1/w_h)^(sigmaL))*(1/(1-b_habit*beta)))^(-1/sigmaC) ) ) ) ^(-1/ ( (sigmaL/sigmaC)+1) ) ) ; % output
d_h = (1 - mc_h)*y_h; % dividends
y_h = d_h + y_h; % Updating y_h in terms of dividend payments (?)
i_h = delta*alpha*(y_h /z_h); % investment
k_h = i_h/delta; % capital
c_h = y_h - i_h ; % consumption
lambda_h = ((c_h - b_habit*c_h)^(-sigmaC))*(1-beta*b_habit);
h_h = (((lambda_h*w_h)*(1/chi_X))^(1/sigmaL)) ; % labor-effort
*******************************************************************
```

Thank you very much for your inputs!