Bertrand Competition

What is Bertrand competition

Bertrand competition is a model of competition between two or more firms, where the companies create a uniform good and compete on price. Theoretically, this price competition leads to the companies selling their products at marginal costs and making no profit since the products are perfect substitutes. The result is also known as the Bertrand paradox, which was originally formulated by Joseph Bertrand in his competition essay of 1889.

Bertrand Competition is a situation when two or more firms sell an identical product and the firm that charges the lower price wins all of the customers. When Bertrand competition occurs, all firms are forced to set equal prices for their products so that they can be on equal level with their competitors. Firms trade off on expensive advertisement and try to get customers by low prices. With this system, firms make zero profits but keep going with hopes of earning profits in some time later in the future. Yet, the firms can not earn profits because they have to set the same price for their products since their products are perfect substitutes. Bertrand competition is a perfect competition leading to zero profits.

Model Assumptions

There are two assumptions in the Bertrand Competition Model. First of all, we assume that the companies are selling a homogenous product such as toothpaste. This means that the product does not have any differences between each other. Secondly, we assume that firms sell their products on a perfectly competitive market. This means that the market is very competitive and has many firms in it, which makes it easy for consumers to switch from one company to another one if they would find something better in some time later. This would give the firms a reason to set their prices lower. There are a lot of reasons that lead to perfect competition, but it all comes down to the fact that firms are competing among themselves and there is no outside influence.

Bertrand-Nash Equilibrium

Firms set their prices equal to marginal costs and experience a loss in the distinctive Nash equilibrium of the Bertrand competition model. Let’s try to figure out why this occurs. Assume that two businesses engage in price-setting competition while producing a homogeneous product at constant marginal costs, denoted by the symbol c. Customers choose the company with the lowest price because they see the products offered by the two businesses as exact equivalents. If businesses charge the same price, then we will assume that demand is shared equally.

If there are no fixed costs, the profit of firm I is calculated as i=(pic)Di(pi,pj), where Di(pi,pj) represents the demand encountered by firm I if firm I charges price pi and firm j charges price pj. The pricing of both firms’ products determine the demand Di(pi,pj) that firm I faces: 1. Firm I has no demand and earns no profit if it charges a higher price than firm j (pi>pj), which results in all customers choosing firm j. 2. All customers will purchase from firm I if firm j charges a greater price than it does (pj>pi), and firm I will benefit by i=(pic)D. (pi). 3. Demand is distributed equally between firms I and j if they charge the same price (pi=pj), and firm I earns a profit of i=(pic)12D. (pi).

So why do businesses, in an equilibrium market, set prices based on marginal costs? Imagine two companies—call let’s them Airbus (firm A) and Boeing (firm B)—produce the same passenger plane for 10 (million) US dollars in marginal expenses in order to better grasp this. Customers purchase goods from the business with the lower pricing. Let’s imagine Boeing demands a price that is 50 million dollars per plane (pB=50) or more over marginal costs. In this case, Airbus has three possibilities. The price it charges can be the same, higher, or lower. Because all clients would continue doing business with firm B, a higher price is obviously not very reasonable. When two businesses set the same price, they share the market’s demand equally and each earns a profit of i=(pc)D(pi)2=20D. (p).

If firm A charges less than pB, the utmost price it can set is 49.99 million US dollars, which is slightly less than firm B’s price in order to attract all clients. Now that the entire demand has been met, Airbus makes a profit of A=39.99D. (pA). If firm A charges a price that is just marginally less than firm B’s pricing, this profit is more than the shared profit at equal prices.

Naturally, though, if Airbus charges a price that is a little lower than Boeing’s, there will be no market for Boeing’s products and Boeing will lose all of its money. It can meet all demand and turn a profit by setting a price that is just a little bit lower than Airbus. To put it another way, each business seeks to undercut its rival’s price in order to satisfy all market demand. Only when charging less does lowering profits stop, which occurs when pricing is equal to marginal costs, does the motive to undercut the competition go. The other firm cannot reasonably charge a greater or lower price if the competitor prices at marginal costs.(At a price above the firm’s marginal costs, the firm has no clients; at a price below the firm’s marginal costs, it loses money.) This outcome is irrespective of the number of firms in Bertrand competition, which means that even if there are only two firms in the market, prices are equal to marginal costs and profits are zero (as in perfect competition).

Image source: https://inomics.com/

Take a look at the image above for the optimum response functions of symmetric businesses in a Bertrand game. For a particular price p1, the blue line represents the best reaction function of firm 2 and the green line, the best response function of firm 1; pM stands for the monopoly price. If you look attentively, you can see that the green line, which indicates where both firms charge the same price when it is above marginal costs and below the monopoly price, is just below the 45-degree line. Firm 1 will charge a price that is marginally less than any price set by firm 2 during this time. This also applies to firm 2, of course. The ideal reaction functions are upward sloping since each company will raise its prices in response to a competitor’s increase in pricing. The unique Nash equilibrium of the game is represented by the junction of the two lines (the red dot). Firms are only playing a mutual best response at one time, and given the competitor’s price choice, no firm has an incentive to vary. This is the moment where the price equals marginal costs, as seen in the figure.

Ending Words

By this point, you should hopefully have a pretty good idea of what a Bertrand equilibrium is, what happens when prices are not in equilibrium and why firms set their prices equal to marginal costs when pricing. Although you might want to know what happens when one or more firms do not follow marginal costs, the whole point is this article is to help you understand the basic theory behind Bertrand competition. In the real world, it is hard to say whether or not businesses actually engage in price-setting competition since they are usually quite secretive about their internal operations. One thing we can be sure of, though, is that competition will be fierce in a free market where consumers and suppliers are completely free to act as they wish.

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Sources

Inomics,com