> All those functions all lead back to how difficult of a problem you are solving for them.
No. 1) The market size is independent of the hardness of the problem. 2) The hardness of the problem is independent of the customer's pressure to solve the problem [1]. 3) Even if a customer has a pressing problem, their budget for your product has a hard upper bound: their revenue. In reality it's nearly always several orders of magnitude lower than that. 4) Good marketing and sales has a strong influence on the perceived value your product creates for the customer, which in turn is the primary factor to determine the price you can ask from a specific customer; the perceived hardness of solving that problem is irrelevant to them.
[1] For example, solving the Travelling Salesman Problem in polynomial time is generally incredibly hard, probably even impossible, and yet solving it would be pretty inconsequential for logistics companies, because they have heuristic algorithms which are good enough.
1) I mentioned your market share increases, not market size. Increasing market share has the same effects as increased TAM. I 100% agree that value is not always directly related to the difficulty of problem you are solving. I think we are talking past each other here. When I say hard problem, it's also assuming this hard problem is a big enough problem for the customer to pay for, not for something "pretty inconsequential"
2) A problem is still a problem that your customer is looking to solve. Because it's a hard problem, it's unlikely they have a solution for it. I wouldn't call it pressure–opportunity sounds better which leads to you getting paid
3) That is correct but what's relevant here is what percentage of that revenue the customer is willing to give up
4) It does but marketing/sales is a lot easier when you are solving a hard problem. You don't need to invest as much into marketing/sales when solving a hard problem because there is less noise and competition. Word gets around much easier
No. 1) The market size is independent of the hardness of the problem. 2) The hardness of the problem is independent of the customer's pressure to solve the problem [1]. 3) Even if a customer has a pressing problem, their budget for your product has a hard upper bound: their revenue. In reality it's nearly always several orders of magnitude lower than that. 4) Good marketing and sales has a strong influence on the perceived value your product creates for the customer, which in turn is the primary factor to determine the price you can ask from a specific customer; the perceived hardness of solving that problem is irrelevant to them.
[1] For example, solving the Travelling Salesman Problem in polynomial time is generally incredibly hard, probably even impossible, and yet solving it would be pretty inconsequential for logistics companies, because they have heuristic algorithms which are good enough.