So, now we've come to the point in our analysis that we're going to look at willingness to pay, right? We've had a lot of build up to this point, we've looked at willingness to pay with surveys and I’ve shown you a lot of other things that a conjoint analysis can do. And I promised you it can give you willingness to pay and it can. So we're going to do an example of that right now. So, lets look at a particular golf ball that we're considering. We've got the magnum force, 10 yards further than the average, $8.99. By now I think you know where these utilities are coming from and that this is just the sum of all those utilities. And we're going to ask ourselves a question, how much more would the average golfer be willing to pay for an increase in distance of 5 yards, okay? So, there it is. It's a little more complicated than what we've done before but, it's not a lot more complicated than what we've done before. Here are the basic steps. The first thing we need to do is calculate the utility gain for the increase in distance. So, we're going to give the ball five more yards or engineer said they can do that. We need to figure out how much happier people will be with that new ball, we calculate it. Then, we're going to find the new price, and it's going to be a bigger price, right? We're going to give them a better ball, we're going to charge a bigger price, we need to find that new price such that we take back from the consumer the exact amount of utility that we gave them when we gave them that improve ball. And so in that sense, it's like a break-even. We give them some utility and whatever that utility is we come over to here to price and we take it back from them. And the difference between that new price that we calculate and the old price is really that increase in willingness to pay. So let's apply this to the data. So first of all we're going to calculate the utility gain for an increase in distance. And that's 0.36- 0.12. Where does that come from? Well if you look at distance, 0.36 is that 15 yards further. That's the new ball, right? because our current ball is 10 yards further. The new ball would be 15 yards further. That would give them a utility of 0.36, and then we subtract the original utility, which is that 10 yards further ball, which is 0.12. So we have a difference of 0.24. So now what are we going to do? We're going to take that 0.24 back in the utility from the price. And how do we do that? Well we know we're going to pay back 0.24, but 0.24, that difference is not exactly the same as the difference between any of the price points that I've got in front me, right? In particular, we're charging $8.99 per ball right now, and we're asking how much more would people be willing to pay? It would be very nice if the $10.99, the utility for that was just 0.24 less than the $8.99, right? And then we could just say, it's $2 and it's very easy because we give them 0.24 in distance, we take 0.24 in utility on price. And all of those numbers are just in front of us, but usually it doesn't work out that way. And in fact, I bet you can tell by looking at the data, the new price is going to have to be somewhere between $8.99 and $10.99 because the spread of the utilities, which is the difference between negative 0.83 and negative 0.08 is greater than 0.24. So here's how we handle that. We know the new price is going to be up in the $8.99 to $10.99 range. We can tell that because the 0.24 is smaller than the overall range between $8.99 and $10.99. What we need to determine is exactly how far into that range we need to go? And then in order to do that we essentially convert it into percent along that range. We do that by taking 0.24 and dividing that by the spread in the two price points that we're interested in. In this particular example that's $8.99 and $10.99 because we know that price is going up and that's why we're moving to the $10.99 price point. That's given right down here. So the resulting calculation gives you 32%, that means we're moving 32% up in that price range. That's what we need to do in order to break even and take back from consumers the exact dollar amount that's equivalent to the utility gain that they get on the distant side. I then take that 32% and multiply it by the difference between the two price points, $10.99 minus $8.99, so $2. And when I make that calculation I get $0.64. And how do I interpret $0.64? That is the increased willingness to pay for the increase in distance. And you can do that for different segments, you can do it for different balls that you might be considering, not just increases in distance. You can even do it for decreases in attributes, suppose you take something away from consumers. The exact same math will tell you how much less they would be willing to pay. This is a very common and very useful set of metrics that comes out of a conjoint analysis.
