Exercise: Information and Market Failures

Goal To create a model/graph depicting necessary conditions for a market to exist when quality is uncertain; in order to understand assumptions and different interpretations for all market models.

Materials
At least one laptop or tablet running a spreadsheet application for each group.
Individuals or groups of 2 or 3 students working on a single computer.
You will need basic knowledge of: spreadsheet calculations, sum, addition, multiplication, bracket rules, cell ranges, relative cell references, absolute cell references etc.

Up to one hour to complete depending on class size, i.e.
20-30" to create models.
10-20" to present and interpret.

Instructions
Open and save a spreadsheet: enter formulae, values and calculations to create a graph of the classic price/demand model.

a) Enter the following data in columns and generate line or scatter graphs:

1. An index, e.g. from 1 to 50.
2. A variable q representing the quality of used cars, randomly distributed over the interval [0, 1]. You might use the rand() function to generate this value.
3. Assuming buyers are prepared to pay up to 1.5 times the suppliers reserve price... Add a column 1.5*0.5 = 0.75. Valuation if everyone values equally assuming average quality (1/2) then buyers are prepared to pay a hypothetical average price 1.5*0.5 = 0.75 

Your graph should look something like this:

fig 1. The problem of uncertainty and the market mechanism

b) Add a column for valuation if buyers had perfect quality information and were prepared to pay p = 1.5*q. 

Your new graph should look something like this:

fig 2. If customers had perfect information...

And if you sort the market index on actual quality the graph should look something like this:

fig 3. If a potentially perfect buyer/supplier matching mechanism existed...

Questions:

What do you think the models represent?
What does the 'index' represent?
What changes if you use an index from 1 to 100, 1 to 1,000,000?
Why did use the random number function to generate the quality value?
What is happening if you sort the market index based on actual quality? (other than generate a more appealing graph) Perhaps you are adding something?