Academic journal article Atlantic Economic Journal

Dynamic Restrictions on Movement of Prices Due to Homogeneity of Demand

Academic journal article Atlantic Economic Journal

Dynamic Restrictions on Movement of Prices Due to Homogeneity of Demand

Article excerpt

Demand of goods is known to be homogeneous of degree zero in prices and income, so that if all prices and income in the economy increase by the same factor, then the demand of goods will remain unchanged. Interestingly, in a case of an efficient capital market combined with constant elasticity demand and a technology with constant returns, homogeneity also implies that all prices within an industry must move together. In particular, if in an economy with N industries (j = 1, ..., N), each with [N.sub.j] firms (i = 1, ..., [N.sub.j]), all firms change prices then, for any two firms i and h, either [Mathematical Expression Omitted].

The proof is simple. Firm i's quantity demanded [Mathematical Expression Omitted], is a function of all prices in the economy and income m. Differentiating [Mathematical Expression Omitted] totally with respect to time:

[Mathematical Expression Omitted] and

[Mathematical Expression Omitted],

j = J if firms i and h are in the same industry. Dividing (1) by quantities:

[Mathematical Expression Omitted],

where [Mathematical Expression Omitted], [Mathematical Expression Omitted], [Mathematical Expression Omitted], and [Mathematical Expression Omitted]. [[Epsilon].sup.ii] [[is greater than] 1] and [[Epsilon].sup.ih] [[is less than or equal to] 0] are firm i's own and cross price elasticities, and [Mathematical Expression Omitted] is firm i's income elasticity. …

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