رقابت ناقص در مدل تعادل عمومی قابل محاسبه - برای اولین بار

Economists normally view the field of imperfect competition in general equilibrium as an open Pandora's box of theoretical and practical problems. For example, how should the oligopoly markup be calculated in models where producers sell some faction of their output to multiple purchasers, which often is the case in applied models based on an input/output structure? How do we calculate the general equilibrium elasticities of demand? Is the choice of numéraire important for the results? Many economists introduce imperfect competition in their applied models with a simple markup based on a Marshallian approximation of demand ignoring these problems. This may result in mis-specified models and possible wrong results. We seek to provide practical solutions to the three problems.

Economists normally view the field of imperfect competition in general equilibrium models as an open Pandora's box of theoretical problems, but an increasing number of policy questions require that we incorporate imperfect competition in our models. Multinational firms, for example, cannot be analyzed in a model with perfect competition, as the multinationals are associated with increasing returns to scale created by knowledge-based assets (Markusen, 1998). Competition policy is another issue that the traditional models with perfect competition cannot analyze. The main theoretical problems in models with imperfect competition relate to how the optimal markup should be determined. They can be summarized as follows: what is the optimal markup when we have more than one buyer, and the buyers have different elasticities of demand? How do we calculate the elasticities of demand in a general equilibrium model? Is the choice of numéraire important for the results? Many economists introduce imperfect competition in their computable general equilibrium models (CGE) with a simple markup on marginal costs.2 Most of these modelers ignore the third problem and get around the first two problems by using large group monopolistic competition where the scale of individual firms and the elasticity of demand are identical and fixed (see for example Gasiorek et al., 1992). Another way of getting around the two first problems is to assume isoelastic demand and linear cost functions, which also results in fixed and well-defined markups (see for example Cox and Harris, 1985). Finally some ignore all of the problems and simply use the final consumer's elasticity of demand in their markups (see for example Harrison et al., 1997). However, the large group assumption and isoelastic demand do not readily apply to all industries and consumers. We need practical solutions to the three problems within the more general Cournot competition to be able to meet the increasing demand for CGE models with imperfect competition. We offer several such solutions in this paper. The first problem is a matter of heterogeneous demand. Many CGE models are based on an input/output structure with several buyers of the same good. Different buyers may have different elasticities of demand, and the producer needs to allow for this to maximize profits. The solution is simple if the producer can price discriminate among all the buyers, but this is often not so. Section 3 derives the optimal markup for a producer with different buyers. The second problem relates to the difference between the Marshallian elasticity of demand and the general equilibrium elasticity of demand.3 Most modelers use the Marshallian elasticity of demand to calculate the optimal markup and consequently ignore that changes in a price of an input affect the quantity of the output sold and as a result affects demand for the input. The general equilibrium elasticities of demand capture these effects. Section 4 shows how to derive an analytical expression for the general equilibrium elasticities of demand in models with Leontief production functions.4 The section also provides a numerical method, which modelers can use to calculate the general equilibrium elasticities of demands in models with a more general production structure. The third problem was first raised by Gabszewicz and Vial (1972) and later emphasized by Ginsburgh (1994), who argued (cynically) that in many applied models there might be larger welfare gains from changing the numéraire than eliminating imperfections. In Section 5, we argue that choosing the numéraire freely is economically meaningless. The owners of the firms also are consumers, so firms must maximize the real wealth of the owners by using the owners’ consumer price index as the numéraire and not an arbitrarily chosen numéraire. In applied work we often do not have information on the owners of the firms, so the theoretical correct numéraire is difficult to apply in CGE models. Therefore, Section 5 also looks at how important the choice of numéraire is for the results in applied models.

The introduction posed the following three questions: what is the optimal markup when we have more than one buyer and the buyers have different elasticities of demand? How do we calculate the elasticities of demand in a general equilibrium model? Is the choice of numéraire important for the results? Practical solutions to these problems have not formerly been provided. The first problem is a matter of heterogeneous demand. Many CGE models are based on an input/output structure with several buyers of the same good. Different buyers may have different elasticities of demand, and the producer needs to take this into account to maximize profits. We show that the producer can use a weighted average of the different buyers’ elasticities of demand to maximize profit, where the weights equal the share sold to each buyer. The second problem relates to the difference between the Marshallian elasticity of demand and the general equilibrium elasticity of demand. Most modelers use the Marshallian elasticity of demand because it is simple. They consequently ignore that an increased price of a good reduces the income of the consumer and reduce the output the producers, which use the good as an input. The Marshallian elasticities do not account for this, because they are calculated keeping the income of the consumer and the output level of the firms using the good as intermediate input constant. This is not true for the general elasticity of demand. We derive an analytical expression for the general equilibrium elasticities of demand in models Leontief production functions.9 We also construct a numerical method, which modelers can use to calculate the general equilibrium elasticities of demands in models with a more general production structure. The third problem was first raised by Gabszewicz and Vial (1972) and later emphasized by Ginsburgh (1994), who argued that in many applied models there might be larger welfare gains from changing the numéraire than eliminating imperfections. However, we argue that choosing the numéraire freely is economically meaningless. The owners of the firms also are consumers, so firms must maximize the real wealth of the owners by using the owners’ consumer price index as the numéraire and not an arbitrarily chosen numéraire. We often do not have data on firm ownership, so this theoretical correct numéraire is difficult to apply in CGE models. Therefore, we look at how important the choice of numéraire is for the results in applied models. Ginsburgh (1994) has two monopolies controlling the entire economy. We show that the numéraire is only important if the imperfectly competing sector controls a large share of the economy. The smaller the imperfectly competing sectors are compared with the rest of the economy, the smaller the numéraire problem becomes. In an example in Section 5, one firm controlled 10% of the economy and the numéraire had a negligible effect on welfare. No real life firm control even close to 10% of a total economy in any developed country, i.e. the choice of numéraire does not affect the results in applied general equilibrium models.