Krishnendu Ghosh Dastidar

On the Existence of Pure Strategy Bertrand Equilibrium

SummaryThe paper analyses the existence of pure strategy Nash equilibrium in price competition (or Bertrand equilibrium) in a homogeneous product market when costs are strictly convex and proves that if output is demand determined such equilibrium always exists. This paper also characterises such equilibria and shows that if firms are identical such equilibria are necessarily non-unique. However for firms with asymmetric costs it can be unique or non-unique.

On Third-Degree Price Discrimination in Oligopoly

In this paper we analyse the effects of third-degree price discrimination on output, profit and welfare in a symmetric cost duopoly. We provide sufficient conditions for output, profit and welfare to be higher (or lower) under third-degree price discrimination in a duopoly, compared with a uniform price regime. Comparing our findings with the traditional results on monopoly price discrimination, we show that the output and profit effects under duopoly price discrimination are very different from those under the monopoly case. However, the welfare effects are very similar.

On Stackelberg games in a homogeneous product market

Abstract In a homogeneous product duopoly with concave demand and strictly convex costs we bring together all the standard results of quantity Stackelberg games, provide some new results with price Stackelberg games and compare the equilibrium configuration of the quantity games with the price games. In the price Stackelberg game we show there is a unique SPNE where the leader chooses a lower price than the follower, but both get equal payoffs. We prove that generally quantity Stackelberg games are less competitive than price Stackelberg games. However, we also demonstrate the possibility of a reversal of this result.

Collusive outcomes in price competition

In this paper we provide a sufficient condition for collusive outcomes in a single-shot game of simultaneous price choice in a homogeneous product market with symmetric firms and strictly convex costs. We also prove the counterintuitive result: if the second derivative of the cost function is nonincreasing in output, it is easier to sustain collusion when the number of firms increases.

Is a Unique Cournot Equilibrium Locally Stable

Abstract We consider a homogeneous product oligopoly, where the Cournot equilibrium is regular and unique. We show that for a duopoly, a unique Cournot equilibrium is always locally stable. For a “ n ” firm asymmetric cost oligopoly a unique Cournot equilibrium is locally stable under very general conditions. The sufficient conditions for local stability of a unique Cournot equilibrium are much less restrictive than what the existing literature suggests. For a symmetric cost oligopoly the unique Cournot equilibrium is almost always locally stable, except for a perverse case. Journal of Economic Literature Classification number: L13.

Corruption in a model of vertical linkage between formal and informal credit sources and credit subsidy policy

The present paper develops a model of vertical linkage between the formal and informal credit markets highlighting the presence of corruption in the distribution of formal credit. The existing moneylender, the bank official and the new moneylenders move sequentially and the existing moneylender acts as a Stackelberg leader and unilaterally decides on the informal interest rate. The analysis distinguishes between two different ways of designing a credit subsidy policy. If a credit subsidy policy is undertaken through an increase in the supply of institutional credit it is likely to increase the competitiveness in the informal credit market and lower the informal sector interest rate under reasonable parametric restrictions. Any change in the formal sector interest rate has no effect. An anticorruption measure, on the contrary, may be counterproductive and raise the interest rate in the informal credit market.

Corruption, Efficiency Wage and Union Leadership

This paper develops a model of determination of the unionized wage in the presence of both collective bargaining and an efficiency wage. The efficiency of each worker is positively related to both the wage and the unemployment rate in the economy. The unionized wage is greater than the efficiency wage and the firm finds it profitable to keep the unionized wage as close as possible to the efficiency wage. The union leader who is entrusted with the task of determining the unionized wage charges a bribe from the firm to keep the wage close to this level. The corrupt trade union leader and the management of the firm play a two-stage Nash bargaining game from where the equilibrium unionized wage and the bribe are determined. The analysis leads to some interesting results which are important for anticorruption policy formulation.

Auctions Where Incomes are Private Information and Preferences (Non Quasi-Linear) are Common Knowledge

We consider a two good world where an individual i with income mi has utility function u(x,y), where x belongs to [0,infinity) and y belongs {0,1}. We first derive the valuation (maximum price that he is willing to pay for the object) for good y as a function of his income. Then we consider the following problem. Suppose good x is available in a store at a fixed price 1. Good y can be obtained in an auction. In such a situation we show that bidding ones own valuation is an equilibrium in a second-price auction. With risk neutral bidders and high enough incomes we derive the symmetric equilibrium in first-price and all-pay auctions and show that revenue equivalence fails to hold. With risk neutrality we also show that under mild restrictions, the revenue maximising reserve price is zero for all the three auctions and the all-pay auction with zero reserve price fetches the highest expected revenue. With low enough incomes, we show that under some restrictions, bidding ones own valuation is a symmetric equilibrium even for first-price and all-pay auctions. Here also, the expected revenue is the highest with all-pay auctions.

On Some Aspects of Scoring Auctions

Scoring auctions are important mechanisms for procurement in both developed and developing countries. Till date the literature has mainly dealt with cases where the scoring rule is quasilinear. Very few papers in the literature have dealt with non-quasilinear scoring rules. In chapter 4 we fill this gap. Under some conditions we derive a clear ranking of the expected scores in first-score and second-score auctions. We show how in many cases second price auctions lead to higher expected score. We show with the help of two examples, that while expected score may be higher with second-score auctions, total expected welfare need not be higher.

Effects of Corruption and Incompetence in the Quality Monitoring Process

In many emerging economies there is a lot of corruption and sheer incompetence in the quality monitoring process and this often leads to poor quality of infrastructure and high prices. In chapter 3 we analyze the impact of such corruption and incompetence on welfare and market quality. We construct two models to demonstrate the following: (i) In the first model we show how corruption in quality monitoring process leads to higher prices, lower quality, lower total welfare and market quality. (ii) In the second model we demonstrate how sheer ‘incompetence’ in the quality monitoring process leads to higher prices. While total welfare does not change with such incompetence, the consumers are worse off and the producers are better off. This means ‘incompetence’ transfers surplus from the consumers to the producers.