A Firm with a Patent Facing Consumer Demand

Computing the Potential Value of an Invention

Note: in order to run the simulation referred to in this slide, go here, to the Java Applet version. You will be directed to download the latest version of the Java plug-in.

To measure the total value of a product to society in a given instant of time, we can sum the value that each consumer assigns to the good. This is equivalent to integrating under the standard demand curve. We demonstrate this process to the left. A demand function is specified in the top text field. Press "Go" and this function will be graphed below.

On this graph, the horizontal axis represents the price set on the new product while the vertical axis represents the number of units that would be sold at that price.

Finally, notice the blue circle that has appeared at the bottom. This is an agent that computes the area under the demand curve. That is, this agent is programmed with a primitive integrating capability and will display the total value of the invention, found by integrating the given expression in the first quadrant.

This slide is designed so you can enter in your own demand curves for study. To do this, you must enter in your function as a MiniScheme expression into the text field at the upper left. Note though, that your functions must adhere to certain criteria to avoid errors. Like any realistic demand function, they must be continuous and monotonically decreasing. Additionally, we require the range be [0, 1], so that the entire population of consumers is normalized to 1. Your functions will be automatically truncated to this range. This means that unless the function passes through the first quadrant, the integral will be zero.(2)

For example, you could try (- 1 p) for a linear demand curve, or (/ 1 (power p 2) ) for an inverse square distribution. (exp (* -1 p)) gives an exponential function.

2. These restrictions allow the agent to approximate the integral using Simpson's Rule, and standardize the display. In case the function never actually reaches zero, the integral is automatically taken in the domain from zero until the demand falls within a small window of zero.