1) My experience as a seller on localbitcoins.com tells me that there is a baseline daily demand of bitcoin coming from people who are price-agnostic such as Joe Schmoe who is buying $2000 worth of bitcoin per day for.. something. Maybe remittances. I never ask. But I will tell you that every day he needs $2000 worth of bitcoin no matter what the price is. He doesn't care what the price is. This component of total demand, measured in USD, is inelastic.
2) The second big component of bitcoin's demand is demand from people who are speculating. If bitcoin is in a downtrend and the market is pessimistic this demand can easily dry up to almost nothing. Speculators can take their money and buy some other asset. If everyone is super optimistic about bitcoin, then this demand can skyrocket thousands and thousands of percent and has practically no ceiling. This component of the total demand is extremely elastic.
Supply:
1) There is a fixed supply schedule. Currently, roughly ~3600 coins are created per day in the form of block rewards. Miners choose whether or not to sell part of this, all of this, or none of this. But the maximum amount of new bitcoin that can be put on to the market per day from miners has a ceiling of 3600 coins. If a miner keeps his bitcoin for more than 24 hours or a week after he mines them, he becomes no different from a speculator. So although there's a fixed supply schedule, this component of the total supply is elastic because miners choose whether or not to put mined coins on the market. They can choose to be speculators.
2) Speculators are the second big component of supply. Most bitcoin lays dormant at any given time and most bitcoin are distributed between a small number of big holders. The amount that can move onto the market on any given day from speculators is absolutely enormous. 15 million coins can be put up for sale tomorrow. (In reality, this never happens. Even during the bubble that would've made Satoshi a billionaire and Roger Ver a quarter-billionaire, we didn't see the dumps. Likely because these holders are too smart to dump all at once and suffer extreme slippage.) In any event, this component of bitcoin's supply is extremely elastic.
In the end, the supply is totally elastic and the demand is partially inelastic. We have two extreme scenarios:
1) The price is bouncing along the price floor created by price-agnostic Joe Schmoe because sentiment is very low and miners are selling everything they mine. Speculators are heavily shorting and selling. (It's impossible to calculate what the price floor is, but there is some price floor created by inelastic demand from Joe Schmoe.)
2) When sentiment is very high, we have the supply of coins from miners drying and the supply of coins from speculators also drying. It's hard to get coins at any reasonable price. Speculators borrow heavily to buy.
The Halving:
The next question is what should happen during a halving? It depends on which situation we are closer to. If we are near the floor created by inelastic demand, we would expect the halving to have a big impact. If most mined bitcoin are being sold, and shorters are as short as they can get, then the supply will drastically be reduced when miners have only half as much coin to sell.
But if the price is high and sentiment is high, then the change in supply might be negligible because the supply of coins from (greedy speculating) miners would already be low. It cannot go negative.
Conclusion:
1. Bitcoin has a floor but practically no ceiling. But it's impossible to calculate where the floor is.
2. The effect of the halving really depends on market sentiment at the time of the halving. It could be large or insignificant.