03-09-2019, 09:28 PM

Thanks for the follow-up.

Indeed, I can see that one may argue for changing discount rates affecting the investment cost of technology. But I am somewhat confused about that possibility. If we assume so, and let's say the car would have an NPV of £42,459 when paying annually, and only £30,000 if paying the full amount at once, I think it would be clearly optimal to pay at once. So, shouldn't the model then include the option to pay the full price at once?

On the other hand, if the NPV would be only of £8,868 when paying annually a car bought in 2012, but the full costs of the manufacturers and retailers correspond to the NPV price £30,000, wouldn't they be selling at a big loss if they would accept annual payments that are worth of only £8,868? As a car seller with perfect foresight, don't think I would accept such.

The TIMES documentation on the objective function (written by prof. Richard Loulou AFAIK), states that "if the technology discount rate is equal to the general discount rate, then the stream of ELIFE yearly payments is equivalent to a single payment of the whole investment cost located at year k, inasmuch as both have the same discounted present value." And by definition, if the technology discount rate is not specified, it is equal to the general discount rate. So, to me that would seem to confirm the equivalence principle, although the documentation does not seem to explicitly give much consideration about time-variant discount rates, other than mentioning that they are supported.

The current handling of time-dependent discount rates in the TIMES code was settled by about 15 years ago, in agreement by me and Uwe, who was at that time the primary maintainer. It can of course be changed, if there are good arguments and agreement about that.

Indeed, I can see that one may argue for changing discount rates affecting the investment cost of technology. But I am somewhat confused about that possibility. If we assume so, and let's say the car would have an NPV of £42,459 when paying annually, and only £30,000 if paying the full amount at once, I think it would be clearly optimal to pay at once. So, shouldn't the model then include the option to pay the full price at once?

On the other hand, if the NPV would be only of £8,868 when paying annually a car bought in 2012, but the full costs of the manufacturers and retailers correspond to the NPV price £30,000, wouldn't they be selling at a big loss if they would accept annual payments that are worth of only £8,868? As a car seller with perfect foresight, don't think I would accept such.

The TIMES documentation on the objective function (written by prof. Richard Loulou AFAIK), states that "if the technology discount rate is equal to the general discount rate, then the stream of ELIFE yearly payments is equivalent to a single payment of the whole investment cost located at year k, inasmuch as both have the same discounted present value." And by definition, if the technology discount rate is not specified, it is equal to the general discount rate. So, to me that would seem to confirm the equivalence principle, although the documentation does not seem to explicitly give much consideration about time-variant discount rates, other than mentioning that they are supported.

The current handling of time-dependent discount rates in the TIMES code was settled by about 15 years ago, in agreement by me and Uwe, who was at that time the primary maintainer. It can of course be changed, if there are good arguments and agreement about that.