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A market structure where only one supplier and only one buyer exists is a bilateral monopoly. A bilateral monopoly is the combination of a monopoly (a single seller) and a monopsony (a single buyer) in a market. Bilateral monopoly occurs when there is a containment in the market, that is when there is a limited number of market participants or the option to explore other suppliers is costlier than sticking to a single one.
In a bilateral market, both the buyer and the seller sell to maximize profits. While the seller has the likelihood of inflating the price of products since he is the only supplier, the buyer will also bargain to the lowest price since the seller has no other buyer to sell to.
A Little More on What is a Bilateral Monopoly
Bilateral monopolies were the common practice in the labor markets between the 18th and 20th centuries, especially by developed our industrialized nations. Given that there were limited companies at the period, all jobs opportunities tend to be concentrated in a small or contained region so that the companies can drive lower wages. Workers, who also seek high wages try many options to have higher bargaining powers, such as forming labor unions. The two sides (the companies and the workers) must however negotiate based on the relative bargaining powers they both have, the outcome of the negotiations will determine the wages that will be paid. The common example is such companies are mining companies.
Reference for “Bilateral Monopoly”
Academics research on “Bilateral Monopoly”
Bargaining and group decision making: Experiments in bilateral monopoly., Siegel, S., & Fouraker, L. E. (1960). Bargaining and group decision making: Experiments in bilateral monopoly. Most economic models about bilateral monopoly (1 seller sells 1 product to 1 buyer) predict that the amount sold will be determinate at the amount which maximizes joint payoff, but that the price will be indeterminate. Pairs of Ss bargained over prices and quantities of a hypothetical commodity with real payoffs contingent on success in bargaining. The theoretical prediction was confirmed. In spite of severe restrictions on communication, most Ss arrived at prices which produced a 50-50 division of the maximum joint payoff. Variance of prices was reduced as information increased. The member of a bargaining pair with more information was at a disadvantage, because he arrived more quickly at the equitable offer and so was handicapped in subsequent bargaining. (PsycINFO Database Record (c) 2016 APA, all rights reserved)
Bilateral monopoly, successive monopoly, and vertical integration, Machlup, F., & Taber, M. (1960). Bilateral monopoly, successive monopoly, and vertical integration. Economica, 101-119.
Bilateral monopoly, Bowley, A. L. (1928). Bilateral monopoly. The Economic Journal, 38(152), 651-659.
Bargaining and concession making under bilateral monopoly., Komorita, S. S., & Brenner, A. R. (1968). Bargaining and concession making under bilateral monopoly. Journal of Personality and Social Psychology, 9(1), 15.