Dynamic Commodity Market
The two Competitive Products (Spacely Sprockets and Cogswell Cogs), along with their WTP Customer Distributions, are completely defined by the ‘Product Generator’ node.
The ‘Recursive Loop Start’ node does not need to be configured. The companion ‘Recursive Loop End’ node contains all of the configuration details.
The input to the ‘Recursive Loop Start’ node are the original Prices from the Product Generator.
Price setting is based upon the assumption that the other Competitor maintains their Price from the previous round.
Prices are adjusted downwards very slowly as the Demand Curve shows that each Competitor is already very close to their Profit Maximizing Price (a tiny Price discount will reach it).
In the final round, both Spacely Sprockets and Cogswell Cogs Price their Products at $84.66.
This Dynamic Competition has been configured to loop for 10 iterations (from Iteration 0 to Iteration 9).
At each loop iteration, the Product Prices drop from $150 to $105 to $102.25 all the way down to $84.66. The expected Quantity, Revenue, and Profit are all calculated.
Prices are decreasing but at a slower and slower rate. It will take a large number of rounds of competition before Prices reach Marginal Cost.
At each iteration, the expected Quantity is increasing. But the last data point shows the actual Quantity after both Competitors set Price.
Joseph Bertrand (1852 - 1900)
Suppose two Competitors sell a homogeneous commodity, each with the same cost, so that Customers choose the Product solely on the basis of Price. Demand is infinitely price-elastic because neither Competitor will set a higher Price than the other (doing so would yield the entire market to their rival). If they set the same Price, the Competitors will share the Profits.
However, if either Competitor were to lower its price, even a little, it would gain the whole market and substantially larger Profits. Since both Competitors know this, they will each try to undercut the other until the Product is selling at zero economic profit.
There are several reasons why the Bertrand Paradox is rarely seen in practice:
Capacity Constraints: Competitors often do not have enough Capacity to satisfy all demand from the entire Market. Hence Competitors seek to set Prices above Marginal Costs at the point which all of their Production Capacity is sold. See Also: MS-172 Bertrand–Edgeworth Competition which explores a Price War between Commodity Products where both Competitors have Capacity Constraints.
Search Costs: Consumers suffer Search Costs to find the full range of their options. But when Consumers are unwilling to bear these Search Costs, Price Dispersion can result such that there is variation in Prices across Competitors selling the same Product. See Also: MS-173 Bertrand Competition with Search Costs which explores another variation of Bertrand Competition. The Products in this Market are, again, undifferentiated Commodity Products, but there are Search Costs that limit Customer awareness of each Product.
Product Differentiation: If the Products are different then Customers may not switch to the Product with the lowest Price but will continue to buy those Products that yield the greatest Consumer Surplus. See Also: MS-174 Bertrand Competition with Product Differentiation which explores the limitations of Bertrand Competition when the Products are no longer Commodities but are Differentiated from one another. And See Also: BB-131 Orthogonal Competitive Loop which explores a Competitive Price War between differentiated Products.
Shipping Costs and Geographic Differentiation: If Customers have to pay different amounts for shipping or for acquiring the Product, then they will have a natural bias to buy the commodity Product that is more local to them – even if the local Product is a little more expensive. This bias will ensure that Prices never decline down as far as Marginal Cost and that Competitors can be Profitable. See Also: CS-102 Rise of the Microbrew – Part 02 Local Monopoly which shows how Geographic Differentiation can be a source of Market Power.