I wanted to know whether it is possible/customary to have non-CRS production functions in multisector DSGE models or not. Actually, the problem is that I have an open economy model with multi-sector production. If I have CRS production functions in all of the sectors, I will have full specification and there will be zero production in all sectors except one.
Is there any similar paper that can help?
Sorry, but I don’t understand the question. What exactly is your problem?
Thank you for your reply.
In my DSGE model, I have three representative firms. The economy is open and I have a terms of trade shocks. Because all the firms are CRS, only for a special case of relative prices, all of them will produce a nonzero amount.
I wanted to know is it OK to have decreasing returns to scale production functions? (I edited the above question)
Your question is still not well-defined. If the firms are monopolistically competitive, they will produce non-zero amounts. You are thinking about a perfectly competitive world where the most productive firm will drive everyone else out of the market.
And yes, using decreasing returns to scale is OK.
I should mention that each sector is producing a different good.
For the monopolistic competition case, you mean there is monopolistic competition inside each production sector or between the three sectors?
If inside each sector, does it make a difference? I mean because the Dixit-Stiglitz Aggregator of each sector sells in a competitive market, full specification happens.
I mean between sectors, obviously. If all three goods produced are “essential” in some form, they will be produced in non-zero quantity.
What do you mean by essential?
Can be any monopolistic competition between producers of different goods?
my sectors are 1-nontradable, 2-tradable energy intensive, 3-tradable non-energy intensive
If there is taste for each variety of the three goods, then consumers are going to demand some regardless of price. If they are intermediate goods and subsequent production does require strictly positive amounts of each of these goods, then again, firms will demand some regardless of price.
Thank you so much.
And how we should model competition between sectors? is just being essential enough?
Is there any similar paper?
Take any paper with two sectors, tradables and non-tradables that are combined using a CES-aggregator. For example https://doi.org/10.1111/j.1468-0297.2010.02362.x
Thanks a lot.
By the way, we have two tradable + oil in this economy. A case is were there is zero production of a product but nonzero consumption of that product, as it can be imported. Does in this case, being essential guaranty nonzero production of all the firms?
This is a question I cannot answer, because I did not set up the model. As you can infer from our previous discussion, it depends on the exact setup of the model you built.