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This paper revisits a well-known case of optimal fiscal policy in a Ramsey model where consumer utility is defined over consumption and public goods. We show that normalising the size of the population to one eliminates the scope for active policy-making since the decentralised equilibrium coincides with social planning. Then, we modify the model to allow for a population of N > 1 agents, whereby restoring the role of the government as a policymaker. Both in the Stackelberg case and in the decentralised game, we prove that optimal fiscal policy and consumption are not only time consistent but also subgame perfect.

We investigate dynamic R&D for process innovation in an oligopoly where firms invest in cost-reducing activities. We focus on the relationship between R&D intensity and market structure, proving that the industry R&D investment monotonically increases in the number of firms. This result contradicts the established wisdom acquired from static games on the same topic. We also prove that, if competition is suficiently tough, any increase in product substitutability reduces R&D efforts.

We investigate dynamic R&D for process innovation in a duopoly where firms may either undertake independent ventures or form a cartel for cost-reducing R&D investments. By comparing the profit and welfare perfomances of the two settings in steady state, we show that private and social incentives towards R&D cooperation coincide for all admissible levels of the technological spillovers characterising innovative activity. This results stems from smoothing the investment reffort over the time horizon of the game.

The literature on the time inconsistency of optimal monetary policy puts forward the idea that a central bank may strategically exploit the first mover advantage against the privat sector, manipulating expectations so as to achieve a higher level of employment and output. We argue that this view is largely ill-founded. We show that the dynamic version of the basic model used in the literature is an optimal control model yealding a time consistent and stable solution to the central banker's problem, where prices are stable and the output reaches the full employment level in steady state. Then we extend it to include a strategic privat sector, which transforms the initial setup into a different game. We prove that such a game has a strongly time consistent open-loop Nash equilibrium, as well as a time consistent Stackelberg open-loop equilibrium with the bank leading,where, however, the bank cannot gain as compared to the simultaneous game. With the privat sector leading, inflation may arise in equilibrium if output is below the full employment level.

We reformulate the monetary policy model of Barro and Gordon (1983a) by using an extended game with observable delay where the hierarchy of play between the central bank and the private sector is endogenous. This allows us to endogenise the institutional setup wherein the monetary policy game takes place. We show that positive inflation may be observed due to mixed strategies rather than time inconsistency.

The existing (static) literature stresses the relevance of capital inputs in determining whether any given merger is (i) profitable and (ii) socially efficient, or not. We take a differential game approach to the same issue, proposing two different models based, respectively, on the capital accumulation dynamics introduced by Ramsey and Solow, respectively. We show that the change in the steady state size of productive plants induced by a merger may play a decisive role in determining whether such a merger is profitable, or socially efficient. However, unlike the static contributions in the same vein, we show that the parameter sets where, respectively, firms find it convenient to merge, and the merger is welfare-increasing, do not intersect at all, irrespectively of the capital accumulation dynamics being considered. This entails that a regulator concerned with the welfare performance of an industry should prevent firms from carrying out any horizontal merger

We present a different duopoly game with capacity accumulation, where firms control investment effords and sales, which can be at most equal to the respective installed capacities at any point of time. We use, alternatively, inverse and direct demand functions with product differentiation, recalling Cournot and Bertrand competition. We show that, at the subgame perfect steady state equilibria, Cournot and Bertrand profits do not coincide, unless the game is quasi-static, which happens if capacity does not depreciate over time.

We present a differential duopoly game with capacity accumulation, wherethe closed-loop memoryless Nash equilibrium collapses into the open-loop Nash equilibrium. Sy mmetric Bertrand and Cournot equilibria are observationally equivalent. This result encompasses the conclusions of the well known model Kreps and Scheinkman (1983) concerning the equivalence between the Bertrand and Cournot settings in a static two-stage game. However, in the dynamic framevork, the equilibrium outcome is different, when one firm plays à la Bertrand and the other à la Cournot. This has relevant bearings upon firms` endogenous choice of the market variable, as well as the social desirability of prices vs quantities. For some admissible parameter ranges, the conflict between private and social incentives concerning the choice between prices and quantity disappears.

We investigate a dynamic oligopoly game where goods are differentiated and prices are sticky. We study the open-loop Nash equilibrium, and show that the latter equilibrium entails a larger level of steady state production as compared to the former; both equilibria entail a larger level of production in steady state than in static game. We also study the effects of price stickiness and product differentiation upon the steady state equilibrium allocation. We find that per-firm equilibrium output is increasing in both product differentiation and price stickmess.

We consider a nynamic oligopoly where firms invest to increase product differentiation and an externality effect operates in the R&D activity. We compare the steady state solutions under alternative decision rules, namely, the open-loop and the closed-loop Nash equilibrium. Significant differences emerge, concerning the effect of the number of firms upon the optimal degree o product differentiation. We also compare the privat optima with the social optimum, and derive implications concerning the social diserability of different decision rules.

We consider a differentiated oligopoly where firms compete a la Cournot in the market phase, and each firms may invest in advertising activity, to enlarge its market size. Each firm`s advertising effort has positive external effects on the market size of all rivals. We derive the open-loop (and the coincident closed-loop) Nash equilibrium, and the optimal behavior of a cartel involving all firms setting both quantities and advertising efforts so as to maximize joint profits. The comparative assessment of these equilibria shows that a cartel may produce a steady ste where social welfare is higher than the social welfare level associated wit the non-cooperative setting. This is due to the positive externalities from advertising activity.

We illustrate two di¤erential oligopoly games using, respectively, the capital accumulation dynamics à la Nerlove-Arrow, and the capital accumulation dynamics à la Ramsey. We prove that these games benefit from the property that closed-loop memoryless solutions degenerate into open-loop solutions, since the best reply of a generic firm is independent of the rivals' state variables, which entails that the cross e¤ect from rivals' states to own controls disappears.

We illustrate a differential oligopoly game where firms compete à la Cournot in homogeneous goods in the market phase, and invest in advertising activities aimed at increasing consumers' reservation price. Such investments produce external effects, characterizing the advertising activity as a public good. We derive the open-loop and the closed-loop Nash equilibria, and show that the properties of the equilibria depend on the curvature of the market demand function. The comparative assessment of these equilibria shows that firms' advertising efforts are larger in the open-loop than in the closed-loop equilibrium. We also show that a cartel involving all firms, setting both quantities and advertising efforts so as to maximize joint profits, may produce a steady state where social welfare is higher than the social welfare levels associated with both the non-cooperative settings.

We investigate a differential oligopoly game where firms compete in account Market whose demand function is always downward sloping but can take any degree of curvature. There exist two economically meaningful saddle points, one dictated by demand conditions, the other by the Ramsey rule. In steady state, optimal capital is non-decreasing in market size. Then we show that the socially efficient output is independent of the curvature of market demand. This entails that the welfare loss associated to the Cournot equilibrium decreases as market size increases.