Browsing by Author "Dixon, Huw"
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- Entry and the accumulation of capital : a two state-variable extension to the Ramsey modelPublication . Brito, Paulo; Dixon, HuwIn this paper we consider the entry and exit of firms in a Ramsey model with capital and an endogenous labour supply. At the firm level, there is a fixed cost combined with increasing marginal cost, which gives a standard U-shaped cost curve with optimal firm size. The costs of entry (exit) are quadratic in the flow of new firms. The number of firms becomes a second state variable and the entry dynamics gives rise to a richer set of dynamics than in the standard case: in particular, there is likely to be a hump shaped response of output to a fiscal shock with maximum impact after impact and before steady-state is reached. Output and capital per firm are also likely to be hump shaped
- Entry and the accumulation of capital: A two state variable extension to the Ramsey modelPublication . Brito, Paulo; Dixon, HuwIn this paper we consider the entry and exit of firms in a dynamic general equilibrium model with capital. At the firm level, there is a fixed cost combined with increasing marginal cost, which gives a standard U-shaped cost curve with optimal firm size. Entry is determined by a free entry condition such that the cost of entry is equal to the present value of incumbent firms. The cost of entry (exit) depends on the flow of entry (exit). Equilibrium is saddle-point stable and the stable manifold is two-dimensional. Transitional dynamics can, under certain circumstances, be non-monotonic.
- Fiscal policy, entry and capital accumulation : Hump-shaped responsesPublication . Brito, Paulo; Dixon, HuwIn this paper we consider the entry and exit of firms in a Ramsey model with capital and an endogenous labour supply. At the firm level, there is a fixed cost combined with increasing marginal cost, which gives a standard U-shaped cost curve with optimal firm size. The costs of entry (exit) are quadratic in the flow of new firms. The number of firms becomes a second state variable and the entry dynamics gives rise to a richer set of dynamics than in the standard case: in particular, there is likely to be a hump shaped response of output to a fiscal shock with maximum effect after impact and before steady state is reached. Output and capital per firm are also likely to be hump shaped.
- Fiscal policy, entry and capital accumulation: hump-shaped responsesPublication . Brito, Paulo; Dixon, HuwIn this paper we consider the entry and exit of firms in a Ramsey model with capital and an endogenous labour supply. At the firm level, there is a fixed cost combined with increasing marginal cost, which gives a standard U-shaped cost curve with optimal firm size. The costs of entry (exit) are quadratic in the flow of new firms. The number of firms becomes a second state variable and the entry dynamics gives rise to a richer set of dynamics than in the standard case: in particular, there is likely to be a hump shaped response of output to a fiscal shock with maximum impact after impact and before steady-state is reached. Output and capital per firm are also likely to be hump shaped.
- From Sunspots to Black Holes: singular dynamics in macroeconomic modelsPublication . Brito, Paulo; Costa, Luis F.; Dixon, HuwWe present conditions for the emergence of singularities in DGE models. We distinguish between slow-fast and impasse singularity types, review geometrical methods to deal with both types of singularity and apply them to DGE dynamics. We find that impasse singularities can generate new types of DGE dynamics, in particular temporary determinacy/indeterminacy. We illustrate the different nature of the two types of singularities and apply our results to two simple models: the Benhabib and Farmer (1994) model and one with a cyclical fiscal policy rule
- From Sunspots to Black Holes: Singular dynamics in macroeconomic models : model with endogenous markupsPublication . Brito, Paulo; Costa, Luis F.; Dixon, HuwWe develop a simple Ramsey model with numerous Cournotian industries where entry generates an endogenous markup. The model produces two different regimes: a monopoly and an oligopoly one. We provide a rigorous study of non-smooth dynamics and we also analyse the global dynamics of the model, demonstrating the model exhibits robust heteroclinic orbits, either of the smooth or the non-smooth type. Similar economies may be in any of these regimes and they may change regime along its convergence path. Fixed costs and elasticities of demand, play a crucial role and changing their values may alter the dynamics in a radical way, either by inducing a discontinuous transition or a discontinuous hysteresis.
- Non-smooth dynamics and multiple equilibria in a Cournot–Ramsey model with endogenous markupsPublication . Brito, Paulo; Costa, Luís F.; Dixon, HuwWe consider a Ramsey model with a continuum of Cournotian industries where free entry generates an endogenous markup. The model produces two different regimes, monopolistic and Cournotian monopolistic competition, resulting in non-smooth dynamics. We analyze the global dynamics of the model, demonstrating it may exhibit heteroclinic orbits connecting multiple equilibria. Small transitory changes in parameters can lead to large permanent effects and there can be a poverty trap separating a low-capital and high-markup equilibrium from a high-capital low-markup equilibrium. We apply results from the mathematics of non-smooth dynamic systems, which provide a more general frame-work for understanding regime switching..
- Non-smooth dynamics and multiple equilibria in a Cournt-Ramsey model with endogenous markupsPublication . Brito, Paulo; Costa, Luís F.; Dixon, HuwWe consider a Ramsey model with a continuum of Cournotian industries where free entry generates an endogenous markup. The model produces two different regimes, monopoly and oligopoly, resulting in non-smooth dynamics. We analyze the global dynamics of the model, demonstrating the model may exhibit heteroclinic orbits connecting multiple equi¬libria. Small transitory changes in parameters can lead to large permanent effects and there can be a Rostovian poverty trap separating a low-capital and high-markup equilibrium from a high-capital low-markup equilibrium. The paper applies recent results from applied math¬ematics for non-smooth dynamic systems.