DSGE user guide

In the Dynare DSGE User guide, Can anyone please explain to me, how the equation on marginal cost and the subsequent two equations on wage and rental rate of capital on page 14 has been derived. It is not very clear from the text.

Thanks

From the profit maximization problem of the firm. The marginal cost is the multiplier on the constraint. Take a look at e.g. Walsh’s textbook.