Economics of Being Married & Vacationing
I was talking with Ashley the other day about vacationing. It seemed that everyone around us has, or is, going on vacations all the time. Take for instance my brother Nick. That kid has been everywhere. Not only that, but he travels all the time! He just got back from a trip, with some of his good buddies, to Mexico. Before that, he went on a cruise to Mexico. I am not bad-mouthing it, I am just jealous. Anyways, as Ash and I were talking about vacationing we got stuck on the principle of how to spend money.
My argument was that we spend as little as possible on the hotel, and spend that money elsewhere. Meaning that we would find a comfortable place to put our bags, and depending on the location, spend the money on activities. I think that the fun of the vacation is going places. That is why you left the house in the first place! My ideal hotel would look something like this:

Love Shack
It is not the best looking thing, but you get to spend your money on more things.
Her argument was simple. It was, if you want to have a fun vacation, you better put me in a nice hotel with an awesome pool.
Now honestly her argument is perfectly valid. When you vacation, you are trying to relax. You worked hard, now it’s time to hang out by the pool and enjoy the sun. Her idea of a hotel would be something like this:

Ash's Dream
So this got me thinking, how are Ash’s vacationing preferences, as well as my own, illustrated mathematically? Honestly, I have no idea what the answer is. I just want to jot some ideas down, and see what sort of feedback I can generate.
So to start, I will throw out some parameters that will be needed. They are:
- Probability of Winning the Lotto [L]
- Winnings From The Lotto [t]
- Savings Rate [r]
- Discount Rate [d]
- Wages Earned [w(ICON Health & Fitness)]
- Benefits (money to be spent on vacation) [b(r*w)]
- Time Frame
- I will assume for all time before the vacation there will be 40 periods x ϵ [0,40]
- The vacation will comprise of 5 periods x ϵ [41,45]
And from there, I have can put together (a simple) mathmatical equation.
Ashley’s Present Value of What To Save For The Hotel of Her Dreams = {e^(-dx)*(1-r)*w(ICON)+(L*t)} + {e^(-dx)*b}
You would have to integrate the first part of the binomial from 0 to 40. Likewise integrate the second part from 41 to 45.
Now, you may be asking the question, what does the expected utility for myself look like? It looks like this:
Tyler’s Expected Utility To Save For The Hotel of My Dreams = I DONT CARE, I WANT TO GO ON VACATION!
