A question of formula derivation

General DSGE Modeling
1

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)

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1665213942184825×374 58.1 KB

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.

983d9ad75ca148e51526f8fd8faa8d1
983d9ad75ca148e51526f8fd8faa8d11920×714 73.6 KB

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!

2

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.

3

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

5

Thank you for your help!
I am also confused about the derivation of MC, so I don’t know whether MC is real marginal cost.
Can MC be set to any form I want? Or I can get the form by derivation from certain fomulars?
I try to get MC by using the way I learned in RBC model but I failed.

6

Thank you for your suggestion!
The fomular showed in page13 is familiar with what I want. But I can’t get the goal by repeating the process after the fomular. It seems that Q and Y are replaced in the following process which is different from my goal

7

It says explicitly in the screenshot you posted that MC is real marginal costs. You highlighted that part.

8

Thank you for your help, professor jpfeifer!