Details

Krugman considered the inverse demand function in a general form and that should be chosen such that elasticity of demand decreases with . The usual requirements , also apply. To visualize the model, we take , which provides the most tractable results:

,

where .

One may check that elasticity is decreasing with . Remember that , where is an exogenous population.

Increasing returns in the one-factor case can be modeled as , which is the inverse production function.

To get the total costs function, we need the factor price :

,

so average costs are:

.

In the monopolistic competition case, the following system should be resolved:

.

Interestingly, while solving the system we may simultaneously obtain

and

.

This solution shows how demand walks around the average costs curve while changes (bottom plot). Notice that the number of firms in a growing market also increases, while individual consumption of each good decreases. This means growing diversity and volume of consumption for a representative consumer.

Unlike Krugman's original paper, we put on the vertical axis of the upper plot instead of , but as is exogenous, this does not influence the exposition (we just let the upper plots depend on the parameter).

This model may describe international trade or agglomeration effects because an increase of corresponds to market extension. This simple model ignores transportation costs, but they may be incorporated as well, as Krugman shows in his later works.

Reference

[1] P. R. Krugman, "Increasing Returns, Monopolistic Competition, and International Trade," Journal of International Economics, 9(4), 1979 pp. 469–479. doi:10.1016/0022-1996(79)90017-5.