PRICE AND QUANTITY COMPETITION WITH ASYMMETRIC COSTS IN A MIXED DUOPOLY: A TECHNICAL NOTE

We consider a mixed duopoly in which private and public firms can choose to strategically set prices or quantities when the public firm is less efficient than the private firm. Thus, even with cost asymmetry, we obtain exactly the same result (i.e., Bertrand competition) of Matsumura and Ogawa (2012) if Singh and Vives’ (1984) assumption of positive primary outputs holds. However, compared to endogenous determination of the type of contract without cost asymmetry, our main finding is that in the wider range of cost asymmetry, different type(s) of equilibrium related to or not related to the limit‐pricing strategy of the private firm can be sustained. Thus, when considering an implication on privatization, we may overestimate the welfare gain of privatization because Cournot competition takes place after privatization even though cost asymmetry exists between firms. While the result of Matsumura and Ogawa (2012) holds true if the goods are complements, we find the novel results in the case of substitutes.     

ENDOGENOUS TIMING IN A MIXED DUOPOLY: WEIGHTED WELFARE AND PRICE COMPETITION*

In this paper we analyse the endogenous order of moves in a mixed duopoly for differentiated goods. Firms choose whether to set prices sequentially or simultaneously. The private firm maximises profits while the public firm maximises the weighted sum of the consumer and producer surpluses (weighted welfare). It is shown that the result obtained in equilibrium depends crucially on the weight given to the consumer surplus in weighted welfare and on the degree to which goods are substitutes or complements. We also analyse whether the equilibria obtained maximise the sum of the consumer and producer surpluses or not. Finally we study whether the nationality of the private firm influences the results.     

QUANTITY VERSUS PRICE IN A HOMOGENEOUS PRODUCT DUOPOLY*

In a simple homogeneous product setting, the paper looks at the debate on whether firms should choose quantity or price as their strategic variable. It examines a two-stage game between firms with symmetric costs in which the firms choose the strategic mode of operation in the first period and then, in the second period, price or output are chosen simultaneously according to the mode chosen in the first stage. In this game it is possible to have two Nash equilibria where either both play in quantities or both play in prices. One firm choosing price and the other quantity can never be a Nash equilibrium in the two-stage game. Both choosing quantity is always a Nash equilibrium. Both choosing prices may be a Nash equilibrium only in some situations: the structure of the cost functions decides this issue.     

UPWARD-SLOPING REACTION FUNCTIONS UNDER QUANTITY COMPETITION IN MIXED OLIGOPOLIES*

It is shown that in a mixed duopoly under quantity competition, the public firm's reaction function may be upward-sloping. This is the case with a concave demand function when the public firm attaches to private profits a smaller weight than to its own profits.     

QUALITY AND WELFARE IN MIXED DUOPOLY: EFFECTS OF CAPACITY REDUCTION*

Under rationing of a public service due to its lower price and higher quality, the “privatization” could be regarded as a reduction in the capacity of the public service. We develop a model of mixed duopoly in which the service is vertically differentiated, a public firm is in a Stackelberg leader position, rationing happens, and the market is not covered. In one of two possible cases, it is shown that any reduction in the capacity of a public service will lower total surplus unless the price of the public service is too low and its quality is too high.     

COMPLEMENTS VERSUS SUBSTITUTES AND TRENDS IN FERTILITY CHOICE IN DYNASTIC MODELS*

Demographers emphasize decreased mortality and “economic development” as the main contributors generating the demographic transition. Contrary to previous findings, we show that simple dynastic models à la Barro–Becker can reproduce observed changes in fertility in response to decreased mortality and increased productivity growth if the intertemporal elasticity of substitution is low enough. We show that this is largely due to number and welfare of children being substitutes in the utility of parents in this case. We find that with an IES of one‐third, model predictions of changes in fertility amount to two‐thirds of those observed in U.S. data since 1800.     

A MODEL OF ENDOGENOUS PAYOFF MOTIVES AND ENDOGENOUS TIMING IN A MIXED DUOPOLY*

A model of endogenous payoff motives and endogenous order of moves is analysed in a mixed duopoly. We find that, when a non‐negative price constraint is imposed on public and private firms' quantity choice, both firms always choose to be relative‐payoff‐maximisers, and both simultaneous move and sequential move can be sustained in equilibrium. In contrast, when non‐negative absolute profit constraint is imposed, public and private firms always choose to be absolute‐payoff‐maximisers, and only sequential move can be sustained in equilibrium.     

LOCATION OF PUBLIC FIRM IN THE PRESENCE OF MULTINATIONAL FIRM: A MIXED DUOPOLY APPROACH*

By incorporating a multinational private firm into the mixed duopoly model with Hotelling‐type spatial competition, we show that the private firm's nationality is a matter of the public firm's location. As the share of foreign capital increases in the private (multinational) firm, the public firm moves to a central place. The effects of price regulation and sequential location choice are also discussed.     

ON THE ROBUSTNESS OF PRIVATE LEADERSHIP IN MIXED DUOPOLY

We investigate a mixed duopoly where a state‐owned public enterprise competes against a profit‐maximising private enterprise. We analyse whether private leadership or public leadership is robust in the observable delay game. We find that private leadership is always risk dominant. We also investigate how ownership structure in a public firm affects the equilibrium distribution of roles. We find that the roles are as follows: (1) Cournot, when the degree of privatisation is low, (2) private leadership, when it is middle, (3) both private leadership and public leadership, when it is high. The result implies that private leadership is again more robust.     

IMPERFECT SUBSTITUTES FOR PERFECT COMPLEMENTS: SOLVING THE ANTICOMMONS PROBLEM

An integrated monopoly, where two complements forming a composite good are offered by a single firm, is typically welfare superior to a complementary monopoly. This is ‘the tragedy of the anticommons’. We analyse the robustness of such result when competition is introduced for one or both complements. Particularly, competition in only one of the two markets may be welfare superior to an integrated monopoly if and only if the substitutes differ in their quality so that, as their number increases, average quality and/or quality variance increases. Then, absent an adequate level of product differentiation, favouring competition in some sectors while leaving monopolies in others may be detrimental for consumers and producers alike. Instead, competition in both markets may be welfare superior if goods are close substitutes and their number in each market is sufficiently high, no matter the degree of product differentiation.     

THE PRICE LEVEL, THE QUANTITY THEORY OF MONEY, AND THE FISCAL THEORY OF THE PRICE LEVEL

This paper examines price‐level determination from the perspective of portfolio choice. Arbitrages among money balances, bonds, and investment goods determine their relative demands. Returns to real balance holdings and after‐tax returns to investment goods determine the relative values of nominal and real assets. Because expectations of government policies ultimately determine the expected returns to both nominal and real assets, the price level depends on interactions among current and expected future monetary and fiscal policies. The quantity theory and the fiscal theory emerge as special cases produced by restricting both the margins and the policies considered.     

MARKET‐DEMAND BOOSTING AND PRIVATIZATION IN A MIXED DUOPOLY

This study incorporates demand‐boosting strategies into a mixed duopoly model in order to consider the endogenous determination of market demand. The results indicate equilibrium characteristics that differ from those found under an exogenous demand setting. As consumers become more sensitive to the demand‐boosting strategies of firms, the government must choose a lower level of privatization. This suggests that the responsiveness of consumer demand to the demand‐boosting strategies of firms constitutes a limiting factor for privatization.     

QUANTITY AND PRICE EFFECTS IN AN ANALYSIS OF WORLD TRADE BASED ON AN ACCOUNTING MATRIX*

This paper describes the construction of an accounting matrix for the world economy in 1977, cast along similar lines to SNA National Accounts, but one in which trade flows replace inter-industry flows as intermediate demand. The matrix distinguishes ten regions. Institutional accounts are presented for three of these, the European Community, North America and Japan. This matrix is used to provide the basis of a linear model in which average propensities to import and consume are replaced by estimated marginal propensities. Use is made of standard estimates of the income effects of terms of trade changes in order to distinguish substitution from income effects in the model, and a means is suggested for separating the full as well as the impact effects of a terms of trade change into income and substitution effects. The estimated import equations are used to derive estimates of regional growth rates compatible with external balance in each region. Multiplier matrices are calculated from the model showing regional interdependence of the world economy reflecting the pattern of trade which is identified in the marginal propensities to import. The effects of various aid policies are calculated using the model. It is shown that the cost of aid to any region is radically altered by taking into account the feedback effects of changes in demand. A policy of tied aid pursued by EEC, North America and Japan can actually lead to an improvement in Japan's balance of payments position. Finally the effects of movements in relative prices are illustrated by means of two examples.     

THE EXISTENCE OF EQUILIBRIUM IN A DIFFERENTIATED DUOPOLY WITH NETWORK EXTERNALITIES*

The existence of a pure‐strategy subgame‐perfect equilibrium in qualities and prices is investigated in a duopoly model of vertical differentiation where quality improvements require a quadratic variable cost and network externalities operate. We show that there exists a parameter region where the incentive to predate at the quality stage prevents firms from reaching a pure‐strategy non‐cooperative equilibrium with prices above marginal costs. If network externalities are sufficiently large, a Bertrand equilibrium with zero profits may arise, although the amount of product differentiation is strictly positive.     

THE DECISION TO HIRE MANAGERS IN MIXED MARKETS UNDER BERTRAND COMPETITION*

This paper analyses the decisions of firms as to whether or not to hire managers when there is a public firm competing with a private firm in the product market. It is shown that under Bertrand competition with heterogeneous goods both firms hire managers. This is in contrast with the result obtained under Cournot competition, where only the private firm hires a manager. Moreover, welfare is lower if both firms hire managers than if neither firm does. In contrast, under Cournot competition welfare is greater if both firms hire managers.     

THE INTEGRATION OF A SYSTEM OF PRICE AND QUANTITY STATISTICS WITH DATA ON RELATED VARIABLES

This paper has two main points. First, the usefulness of the industry detail called for in the SNA would be increased if it were altered to facilitate the construction of price and quantity aggregates classified by stage-of-process sectors. Second, the price and quantity data so arranged should be augmented by data on behaviorally related variables classified the same way. The feasibility of the stage-of-process approach is demonstrated by a table showing the high degree to which the U.S. input-output table for 1967 can be triangularized. The analytical usefulness of the approach is demonstrated through analysis of changes in prices, output, unfilled orders and finished goods inventories for primary and for finished goods manufacturers.     

QUANTITY PRECOMMITMENT AND BERTRAND COMPETITION YIELD COURNOT OUTCOMES: A CASE WITH PRODUCT DIFFERENTIATION*

Using a simple model of two-stage duopoly game, this paper shows that Bertrand-like price competition on a differentiated goods market, following a simultaneous endogenous choice of production capacity, yields the Cournot-like outcomes.     

ENDOGENOUS TIMING IN A MIXED DUOPOLY AND PRIVATE DUOPOLY –‘CAPACITY‐THEN‐QUANTITY’ GAME: THE LINEAR DEMAND CASE*

We consider a game of endogenous timing of sequential choice of capacity and quantity with observable delay in a mixed duopoly and a private duopoly. In mixed duopoly, we find that a simultaneous play at the capacity stage or at the quantity stage can never be supported as subgame perfect Nash equilibrium (SPNE); whereas a simultaneous play at each stage turns out to be the unique SPNE in a private duopoly. In mixed duopoly there is multiplicity of equilibria and all SPNEs require sequentiality at the capacity as well as quantity stage.