# Utilization rate of durable goods

Good morning everyone,

I’m modeling an economy where households do not fully utilize their durable goods (let’s say a car) all day. I’m attaching to the durable goods variable a variable called “u” such as in the investment/capital theory. However, I’m seeing that in this theory this utilization rate cannot really be interpreted as a share of time and is fixed at 1 in the steady state meaning that the capital is fully utilized in the SS.

I wondered if I could do the same for durable goods but “u”, the utilization rate of durable goods, would be interpreted as the share of time the households use the durable good stock. u won’t be at 1 in steady state, and it would be comprised between 0 and 1. I would calibrate the model such that u is at, let’s say, 0.25 (households use their durable good stock during 1/4th of a day, so 1/4th of the year in an annualized model). Just checking if this is okay.

Thank you!

Yes, that sounds feasible. What the literature usually does is interpret 1 as the average level of utilization., which corresponds to your 1/4 of the time.

Thanks @jpfeifer

That means that if households use their durable good stock more, this utilization rate can reach values above 1, right ? I’d like my utilization rate to be comprised between 0 and 1 and fluctuate in that interval.

Keep in mind that with perturbation techniques, you cannot restrict variables to be bounded. So you will always hope for an interior solution. That’s what makes the default quadratic specification around some mean quite attractive.

Thanks @jpfeifer . I’m using perfect foresight. Should I still use 1 in SS for the utilization rate and let it fluctuate above or under 1, or can I use 0.25 and restrict its fluctuations between 0 and 1 ?

I don’t think that it will make a big difference in the end. Much hunch is that the two approaches are almost equivalent and only involve a reparameterization.

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Thanks a lot