Salop Circular City Model: Equilibrium Firms and Parameter Impacts

In the Salop circular city model, firms are evenly distributed along the city's perimeter, each producing a differentiated product and competing with others. The shipping cost (td) is incurred for transporting goods from the firm to consumers, with 't' being the shipping cost parameter. This model seeks to determine the number of firms (n) entering the market in a pure strategy equilibrium, assuming a unit perimeter population density and a fixed entry cost (f) for each firm. The zero profit condition, where firms earn zero economic profit in the long run, is also considered.

In this equilibrium, each firm offers a unique product and sets its price equal to marginal cost plus shipping cost. The number of firms depends on 't' and 'f'. Higher shipping costs reduce the number of firms, as they increase production costs and lower demand. Similarly, higher entry costs discourage new firms, leading to fewer competitors.

To find the equilibrium number of firms, we analyze price (p) and quantity (q) at equilibrium. The price is determined by marginal cost (c) plus shipping cost (td): p = c + td

The demand for each firm's product is represented by: q = a - bp where 'a' is the total market demand and 'b' is the demand elasticity.

The total cost (TC) for a firm includes production cost and entry cost: TC = c + f

Under the zero profit condition, revenue equals total cost: q(p - c - td) = c + f

Substituting the equilibrium price and quantity, we get: q(c + td - c - td) = c + f

Simplifying, this becomes: qf = c

Solving for the number of firms (n), we get: n = a / q = a / (a - bf) where 'bf' represents the entry cost per unit of demand. This equation shows that 'n' decreases as 'f' increases. The shipping cost ('t') affects 'n' indirectly through its impact on equilibrium price and quantity.

In conclusion, the number of firms in the Salop circular city model is influenced by both the shipping cost parameter ('t') and the cost of entering the market ('f'). Higher 't' reduces 'n' by increasing production costs and lowering demand, while higher 'f' reduces 'n' by discouraging new entrants. This analysis provides insights into how these parameters shape the competitive landscape within this model.