The Biequilibrium of Goods and Labour Services A Unified Structural Framework for the City

This paper proposes a biequilibrium for the city. The word is one term and not two: it names the single state in which the goods market and the labour-services market clear at the same time, on jointly determined prices, not in sequence. It is realized on the goods price, the interest rate and the labour-service wage, with capacity carried between periods as a state variable. The framework rests on two identities and four functions. The first identity equates goods supply with the return flow of the consumption value chain; the second equates the labour-service demand the chain generates with a supply anchored by the urban subsistence cost. The four functions, demand, supply and the two sides of the labour-services market, are each written explicitly. A consumption kernel connects them: a matrix that routes expenditure by category and returns the local part to households as income. The kernel is not fixed: its retention shares depend on the interest rate and the goods price, so policy moves the object around which the multiplier circulates, and the paper states its net contribution. Three differences follow. Heterogeneous-agent New Keynesian models write the household side and take production as given; the Miyazawa-type multiplier writes a rank-one circulation of income without prices; the Hayekian triangle writes production in stages, leaving consumption outside. The paper joins the two chains, gives the kernel full rank, and makes it an equilibrium object. The scope is one city: a city-level analysis, not a national one, of an open economy. The paper is theoretical, contains no data, and states mechanisms only.