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Ensuring looked-after children have a stable care placement, social worker and school place is vital to good outcomes, so Ofsted places great emphasis on stability when it inspects children's services, writes Jo Stephenson

This article aims to show the mathematical contexts out of which emerged Solow's 1957 article "Technical Change and the Aggregate Production Function." In particular, it seeks to provide some understanding of its most striking feature, namely, the highly aggregate level on which technical change is discussed and the simple way in which it is represented. The approach is similar to Weintraub's (1991) contextualization of Samuelson's Foundations of Economic Analysis (1947), but it will map out the two mathematical contexts in which Solow's 1957 article can be located. Samuelson's concepts of stability provided Solow the tools for the aggregation of technical change. However, Samuelson's concepts were defined in relation to static equilibrium and not to growth. To arrive at his 1957 representation of technical change, Solow successfully applied P. H. Leslie's concepts and tools of population mathematics. The main mathematical concepts around which this development is described are eigenvalue and eigenvector. It is by the use of these two concepts that aggregation of input-output tables was made feasible.

AbstractWe analyze the impact of interest rate policy on financial stability in an environment where banks can experience runs on their short‐term liabilities forcing them to sell assets at fire‐sale prices. Price adjustment frictions and a state‐dependent risk of financial crisis create the possibility of a policy tradeoff between price stability and financial stability. Focusing on Taylor rules with monetary policy possibly reacting to banks' short‐term liabilities, we find that the optimized policy uses the extra tool to support investment at the expense of higher inflation and output volatility.