The way an experiment works is not a guess, but a hypothesis, so let’s take a look at a two-state model.
In the first state, the cost of producing A is zero, and the value of A is one. In the second state the cost of producing B is zero, and the value of B is one. Let’s say that a particular A is produced, and the value of A is $10; the value of another product A is $10, but it’s a different A.
This is a simple, very common problem of interest in economics. For example, let’s say that A is a particular type of dog food, and B is a particular type of dog food. The marginal rate of substitution between A and B is the same for all food types, but the marginal rate of substitution between A and B varies depending on food type. For example, if you buy cat food, you’ll get more cat food than dog food.
We can think of our world as an infinite system of a finite number of food types, each with a set of food types. We could think of our world as a finite universe, with a finite number of Food Types but not in number with each of them. In other words, finite systems of a given number are not infinite. When we think of our world as finite, we’re thinking of the world as finite. And finite size doesn’t mean infinite.
In the finite world, each food type has a different demand for food. In the infinite world, each food type has a different demand for food. In the finite world, each food type has a set of food types. In the infinite world, each food type has a different set of food types. In some sense, the finite world is a larger universe than the infinite world. The finite world is smaller or not infinite. The infinite world is infinite. But not the same.
Marginal rate of substitution is one of the most basic concepts in economics. A food type has a demand for it. If we look at the demand for that food, we can determine the price. The marginal price of a food type is the amount it would cost to buy or sell a food type.
In the infinite world, food is infinite. In the finite world, food is limited. But if you look at food type demand, you can see that any food type with a high enough demand has a high enough price. Thus, in the infinite world, the demand for any food type is limited. In the finite world, the demand for any food type is limitless.
The marginal rate of substitution, also known as the marginal cost of a good, is the number of units of a good you would need to purchase to replace the unit price of the good. For the good we are considering, the marginal cost is the price per unit. When you have infinite wealth and a finite cost, the marginal cost is infinite. Since the marginal cost is infinite for every food type, the amount of food available for purchase would be infinite. So infinite wealth is also infinite demand.
The formula for this is that we multiply $X$ by the marginal cost of the good: $X = P(X\rightarrow\infty)$ for every $X\geq 0.
