# A question of formula derivation

Best wishes to everyone!
When I am deriving the fomulars in [ Tae-Seok, Eiji, 2013, Productivity shocks and monetary policy in a two-country model, Dynare working papers ], I feel confuse of the following question:

Where did the P(H,t+k) colored in blue come from? (as showed in the picture below)

PS:Here use calvo’s way of sticky price and seller cannot change its price with a given probability of θ.

Here is my process of calculability, I use a way learned in class. I cannot get the P(H,t+k) colored in blue.

Here is the paper:(the fomular is in page 10)
3.Tae-Seok, Eiji, 2013, Productivity shocks and monetary policy in a two-country model, Dynare working papers.pdf (348.3 KB)

Thanks for any suggestion and help!

I guess it has to do with the definition of marginal costs. You seem to have set up a nominal Lagrangian as revenue is price times quantity P_HY_H. But then you need to subtract nominal costs as well. If MC is real marginal costs, then Y_HMC_H is still real.

It seems to me you are starting with a FOC, see page 13