Question

What is the primary intuition in the Melitz 2003 model of heterogeneous firms from "The impact of trade on aggregate industry productivity and intra-industry reallocations", when moving from autarky to a trade equilibrium.

Answer 1

The Melitz model is a dynamic industry model that incorporates firm productivity heterogeneity into the Krugman (1979) monopolistic competition framework, and focuses on steady state equilibrium only. The original Melitz (2003) model considers a world of symmetric countries, one factor (labor) and one industry, but it can be easily extended to the setting of asymmetric countries.4 In each country, the industry is populated by a continuum
of firms differentiated by the varieties they produce and their productivity. Firms face uncertainties about their future productivity when making an irreversible costly investment decision to enter the domestic market. Following entry, firms produce with different productivity levels. In addition to the sunk entry costs, firms face fixed production costs, resulting in increasing returns to scale of production. The fixed production costs lead to the
exit of inefficient firms whose productivities are lower than a threshold level, as they do not expect to earn positive profits in the future. On the demand side, the agents are assumed to have Dixit-Stiglitz preference over the continuum of varieties. As each firm is a monopolist
for the variety it produces, it sets the price of its product at a constant markup over its marginal cost. There are also fixed costs and variable costs associated with the exporting activities. However, the decision to export occurs after the firms observe their productivity. A firm
enters export markets if and only if the net profits generated from its exports in a given country are sufficient to cover the fixed exporting costs. The zero cutoff profit conditions in domestic and exporting markets define the productivity thresholds for firm’s entry into the
domestic and exports markets, and in turn determine the equilibrium distribution of non-exporting firms and exporting firms, as well as their average productivities. Typically, the combination of fixed export costs and variable export costs ensures that the exporting
productivity threshold is higher than that for production for the domestic market, i.e., only a small fraction of firms with high productivity engage in exports markets. These exporting firms supply both the domestic and export markets.

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