Jim Y. Jin

Cournot and Bertrand equilibria compared: substitutability, complementarity and concavity

Abstract This paper assesses the view that Bertrand equilibrium is intrinsically more competitive than Cournot equilibrium. We consider an oligopoly model with linear demand, and a mixture of substitute and complementary products. Our results provide support for the conventional wisdom, and also indicate its limitations. We provide counter-examples showing that no clear-cut comparison of prices and quantities is possible without strategic complementarity in either of the two games. However, price competition is indeed more competitive according to the following criteria: lower mark-up/output ratios, larger average output, and lower average price.

R&D COMPETITION AND ENDOGENOUS SPILLOVERS

The paper examines firms’ choices between innovation and imitation in duopoly. We show that in the unique equilibrium asymmetric firms choose the same level of expenditure on imitation and the same ratio of innovative cost reduction to output. We evaluate the marginal contribution of innovation and imitation expenditure by small and large firms to consumer surplus and welfare, and discuss the desirability of differentiated R&D subsidies on innovation and imitation in terms of R&D tax rebates.

Monopolistic competition and bounded rationality

Abstract This paper shows how a market reaches a unique steady state in monopolistic competition. Without knowing anything about strategic interdependence and only perceiving a linear demand for its own product, every firm follows a simple price strategy to maximize its current profit in each period. The strategy is based on a firm’s own cost function, slope estimate, and its sales and price in the previous period. We show that a market with asymmetric and non-linear demand converges to a unique steady state under rather general conditions.

A Comment on "A General Model of Information Sharing in Oligopoly," Vol. 71 (1996), 260-288, by Michael Raith

Abstract I show that concealing cost is the dominant strategy in Bertrand oligopoly, generalising a result of Gal-Or (1986, Rev. Econ. Stud.53, 85–92) and correcting an error of Raith (1996, J. Econ. Theory71, 260–288). Journal of Economic Literature Classification Numbers: D43, L13.

On the microeconomic foundations of linear demand for differentiated products

This paper provides a thorough exploration of the microeconomic foundations for the multi-variate linear demand function for differentiated products, which is widely used in industrial organization. The setting is the standard representative consumer with a quasi-linear utility function. A key finding is that strict concavity of the quadratic utility function is critical for the demand system to be well defined. Otherwise, the true demand function may be quite complex: Multi-valued, non-linear and income-dependent. We uncover failures of duality relationships between substitute products and complementary products, as well as the incompatibility between high levels of complementarity and concavity. The two-good case emerges as a special case with strong but non-robust properties. A key implication is that all conclusions derived in applied economic models via the use of linear demand that does not satisfy the Law of Demand ought to be regarded with some suspicion.

Information sharing about a demand shock

This paper examines two questions in asymmetric Cournot and Bertrand oligopoly with a demand shock. Under which conditions is information sharing a subgame-perfect equilibrium? What is the welfare effect when firms are better off? Given these questions, the normal assumptions in the earlier literature can be relaxed in three ways: demand functions can be asymmetric; a demand shock can affect firms differently; distributions of the demand shock and information signals can be arbitrary. Under these general assumptions, the answer to the first question is: every firms response to the demand shock is stronger when all firms have perfect information than when one firm does so alone; the answer to the second question is: social welfare increases in Cournot competition, and consumer surplus decreases in Bertrand competition.

Innovation announcement with vertical differentiation

Abstract The paper studies the timing of innovation announcement in a vertically differentiated industry. The high quality firm introduces new products when they become profitable. The new products can be announced early or late. Under an early announcement policy the low quality firm knows the outcome of innovation when choosing its own quality. Under a late announcement policy, however, the low quality firm can only choose its quality based on the distribution of innovation outcomes. The quality decisions are followed by price competition. It is shown that an early announcement policy is socially desirable but incompatible with the interest of the innovative firm.

Free Trade vs. Autarky under Asymmetric Cournot Oligopoly

The paper compares free trade with autarky in an asymmetric multi-country world with Cournot competition, constant returns and linear demand. We first derive conditions for free trade to hurt a country’s consumers, to benefit its firms, to induce it to export, to increase its output, and to raise its welfare. We further show these conditions are linked in a clear order, with each one implying the next. We then demonstrate that with different reservation prices trade can reduce world output and total consumer surplus as well as world welfare and correct oversights in earlier findings by Dong and Yuan (2010).

Free Trade vs. Autarky in an Asymmetric Cournot World

The paper first demonstrates that in a simple asymmetric n-country world with Cournot competition, constant returns and linear demand, free trade can reduce world welfare as well as total output and consumer surplus. We then derive precise conditions for free trade to raise a country’s welfare, consumer surplus, profits etc. and demonstrate how these conditions are linked in a clear order. We also show that free trade always raises the sum of social welfare and consumer surplus in every country. Finally, we show that with symmetric costs or free entry and exit, there are always global gains from free trade.

A Comment on 'The Loss from Trade Under International Cournot Oligopoly with Cost Asymmetry' by Dong and Yuan (2010)

This note corrects some oversights in Dong and Yuan (2010). We show, in particular, that their condition for intra-industry trade to reduce global welfare can never be satisfied. Using a new example, we demonstrate that, nevertheless, their fundamental insight remains correct: Under Cournot competition, trade can reduce global welfare when firms and countries are asymmetric.