What’s the point of extracting implied probabilities from options on federal fund futures?

I like telling fantastical story analogies. So here’s my attempt at explaining what’s the point behind extracting implied probabilities from option prices.

The story goes like this: Let’s say you worked for an arms and munition plant - R&D side of course. And that for some strange inexplicable reason you were caught in an airstrike while driving home one day. Now the missile that’s streaking across the sky is carrying 1000 high explosive anti-personnel bomblets designed to penetrate soft-skinned vehicles (like the one you’re driving for example). From your lab tests at work, and hours spent analyzing bomb dispersal patterns, you have a pretty good guess of the effective dispersal pattern of those bomblets. Given the missile’s trajectory (you had a sensor installed in your car which tracks the movement of Air-to-Ground missiles being fired), you can guess which areas, ceteris paribus, would encounter the greatest concentration of bomblets.

By analogy, the missile’s flight trajectory is the possible direction of interest movements – i.e. either it goes up, down or remains at the same level. Your market macroeconomic indicators are your missile/ interest rate sensors. That bomb dispersal pattern that I was talking about, are my implied probability distribution functions. I want to map out which levels are interest rates most likely to climb or fall to.

In this case I’m looking to map out the regions of probabilities that the interest rate would climb to levels A, B or C.

Laspayre's Index: What they don't tell you about the CPI

Here's a doodle from a tutorial.

Vaguely, the tutorial was about Consumer Price Index and alternative measures. The one currently in use in Australia is based on Laspayre's Index.

To calculate how well off you are after a price hike, you compare 2 ratios: Laspayres Index and Money Income. To calculate Laspayre's index, you take this year's prices and multiply that with last years mixture of goods. Divide that by the base year prices and quantity of goods. Next, you compare that ratio with the ratio of money income (simply, take this year's prices X this years goods and divide by base year prices and quantities.)

If it so happens that your Money Income ratio is less than Laspayre's Index that means you're worse off.

The reason why you multiply it with last year's mixture of goods is because people 'prefer' their old consumption patterns and therefore find it hard to change. Its all part of revealed preference theory.

Anyway, to get the analogy across, economists spend a lot of time thinking about how to compensate people with enough income to leave them just as they were last year. They aim to compensate people for the loss in welfare due to a hike in prices.

Now what they don't tell you is that one of the key assumptions is that they've assumed that people are inflexible and rigid in their consumption patterns. Therefore, the goldfish with a frown in a leaky bowl. (See Diagram Left Rectangle.)

Now what if people adapt to higher prices and substitute away from old quantities of goods that have gone up in price and chose new quantities of goods. What happens to our measures of how well off we are after a rise in prices?

The goldfish with the multi level, worm-hole fishbowl has got choices and though water levels may fall (analogy to welfare falling) he can still get by and choose other modes of consumption.

So I wonder if instead of worrying about compensation for loss of welfare with price hikes, why not give a person more choices instead?