### Introduction

In the United States, healthcare is extremely expensive. Most people could not afford healthcare if they don’t have insurances. In this blog post, I developed two extremely simple dummy models to describe how the prices could be different depending on the development mode of the industry, trying to explain why the products from the pharmaceutical industry are “unreasonably” expensive. The dummy models could be nowhere close or accurate to describe the entire economical process. However, at least to some extent they gave some qualitative and quantitative ideas.

### Models

We have $n$ products to develop and testify. We know (at the end) the $m$ products will be eventually approved or verified, and go into the market. We assume that there are only two possible models for each industry.

#### Model I

Each product was developed by a single independent company. The cost of the development and test for each product is $c$, the price of the product selling in the market is $kc$, where $k$ is revenue coefficient.

#### Model II

There are $h$ big companies that acquire the products being developed from small companies. The big company would take the risk of development failure. Each big company evenly got $\frac{n}{h}$ products, and $\frac{m}{h}$ products would be approved. The cost of the development and test for each product remains the same, which is $c$. The true cost for each product approved would be $\frac{cn}{m}$. The price of the product selling in the market would be $\frac{kcn}{m}$, where $k$ is the revenue coefficient.

### Basic Analysis

#### Total Cost

The total cost or investment to the $n$ products are the same in Model I and II, which is $nc$.

#### Revenue Coefficient and Product Price

If we assume $k$ is only determined by the number of products and their product properties in the market, the value of $k$ used in Model II should be the same as the $k$ used in Model I.

With the same value of $k$, $c$, $n$, and $m$, the prices of the products developed in Model II would be then $\frac{n}{m}$ times more expensive than the products developed in Model I.

In some countries, such as China, the price of the product would be administrated or adjusted by the government to make sure that it is not too expensive, therefore we could assume that the value of $k$ in Model II would be much less than the value of $k$ in Model I for some countries.

In other countries, such as the United States, the government would not interfere with the product price, therefore $k$ remains the same in Model I and II.

#### Number of Companies

In Model II, we actually implicitly assume $m > h$ or even $m \gg h$. However, if $m \ll h$, Model II is not valid and only Model I could be used.

### Pharmaceutical Industry vs Other Industry

#### Model Selection

In the pharmaceutical industry, there are actually only countable pharmaceutical giant companies that are developing all the drugs in the world. Small pharmaceutical start-ups would start the development of the drugs and later sell the drugs to the pharmaceutical giants for further development and evaluation. $m \gg h$, so definitely we have to use Model II to describe the pharmaceutical industry.

In other industries, depending on the value of $m$ and $h$, it could be a Model I industry. With the same value of $k$, $c$, $n$, and $m$, the price of the Model II industry is much more expensive than the price of the Model I industry.

#### Development Cost

The development cost $c$ for a single product in the pharmaceutical industry is much higher than most of the products in other industries.

#### Success Rate

The success rate, $\frac{m}{n}$, in the pharmaceutical industry is much lower than most of the products in other industries.

### Conclusions

Taken these together, because the pharmaceutical industry could be described using Model II, $c$ is much larger, $\frac{m}{n}$ is much smaller, compared to other industries, and in some countries with free markets, $k$ is not adjusted, the price of drug and healthcare would, therefore, be extremely high.