# Imperfect competition (Outdated)

The need to consider imperfect competition and economies of scale when assessing the consequences of trade liberalisation episodes has been widely documented are generally considered to be perfectly competitive with constant returns to scale. Oligopolistic competition is thus assumed to hold in the other sectors, with horizontal differentiation of products and increasing returns to scale, in the line of (Paul R Krugman, 1979) theoretical model and of (Alasdair Smith, Anthony J Venables, 1988) applied partial equilibrium model.

## Imperfect competition in MIRAGE

Imperfect competition is an option that can be activated in the standard version of MIRAGE.

The specification is very close to that used by (G. W. Harrison, T. F. Rutherford, D. G. Tarr, 1997). Each firm produces its own and unique variety. The marginal production cost is constant at given factor prices, and production involves each year a fixed cost, expressed as a fixed quantity of output. Within each sector of each region, firms are assumed to be symmetrical. They compete in a Cournot-Nash way, i.e. they suppose that their decisions of production do not affect the volume of production of their competitors. Moreover they rule out the possibility that their production decision may affect the global level of demand through a revenue effect (the so-called Ford effect). However, firms take their market power into account: following the Cournot-Nash assumption, their decisions can influence the sectoral or infra-sectoral price index (given the above-defined demand structure).

From the absence of strategic interaction implied by the Cournot-Nash hypothesis, it follows that the mark-up is given by the Lerner formula:

$$\quad \mu_{i,r,s}=\frac{P_{i,r,s}}{\mathit{MC}_{i,r}}=\frac{1}{1-\frac{1}{\varepsilon^P_{i,r,s}}}$$

where $\mu_{i,r,s}$ is the mark-up applied in region s by each firm of sector i producing in region r, $P$ is the corresponding price, $MC$ is the marginal cost of production (which does not depend on the market). Time subscript t has been omitted for all variables, for greater convenience. $\varepsilon^P_{i,r,s}$ is the price-elasticity of demand, as perceived by the firm based on the above-mentioned assumptions; it increases with the elasticity of substitution between good i varieties produced in country r (this elasticity is a higher bound for $\varepsilon^P_{i,r,s}$) and with the elasticity of substitution between good i baskets from region r and from other regions; it is a decreasing function of the number of firms in sector i of region r, and of the global market share of region r 's producers taken together in the region s 's market for good i. This endogenous determination of firms' mark-up (already present, in a generic form, in Krugman, 1979), allows the pro-competitive effect of trade shocks to be accounted for.

Changes in the number of firms are also an important matter: it affects competition and therefore will have an impact on markup rates, particularly when the number of varieties is small; it is also important through the preference of firms and final consumers for variety. In MIRAGE, the number of varieties adjusts at each period to match a zero profit condition.

## Calibrating imperfect competition parameters

This formulation requires three types of parameters, describing respectively products substitutability, scale economies and competition intensity. Since these parameters are linked by the zero-profit condition in each sector, only two of them are usually drawn from external sources, and the third one is calibrated. This method is not fully satisfactory, either in terms of consistency or of robustness. This is why a different method is used in MIRAGE, that takes advantage of the whole available information for these three sets of parameters, not only about their value, but also concerning their variance. Once external estimates are collected for the three parameters, their calibrated values are jointly determined such as to minimise their distance from these estimates, subject to the consistency constraints imposed by the model. The inverted variance is used as a weight in calculating this distance, so as to make the adjustment borne more strongly by parameters the less precisely estimated.

For more detailed informations, see Appendix 3 in CEPII Working paper No.2002-17

^{^}Paul R Krugman, 1979. Increasing returns, monopolistic competition, and international trade.

*Journal of international Economics*, 9, Elsevier, pp.469–479.

^{^}Alasdair Smith, Anthony J Venables, 1988. Completing the internal market in the European Community: Some industry simulations.

*European economic review*, 32, Elsevier, pp.1501–1525.

^{^}G. W. Harrison, T. F. Rutherford, D. G. Tarr, 1997. Quantifying the Uruguay round.

*The Economic Journal*, 107(444), pp.1405-1430.