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• We propose a framework for the optimal supply of forest biodiversity. • We define optimal wood and biodiversity streams to maximize social welfare. • Climate change has important implications for biodiversity-oriented policy mechanisms. • Current management undersupplies biodiversity and is inefficient under climate change. Forest biodiversity underpins social welfare by preserving ecosystem multifunctionality and the provision of ecosystem goods and services. Still, the social value of biodiversity is not adequately incorporated into forest management and decision support models. This study proposes a novel approach for defining socially optimal biodiversity levels, wood supply and taxation schemes under climate change. We developed a partial equilibrium model to maximize consumers' and producers' surplus until the end of the century, including climate change impacts as productivity shocks in a coupled ecological-economic framework. In our model, we consider a first-best and a second-best taxation scheme to internalize the value of forest biodiversity into forest planning. The framework developed here was applied to a temperate forest landscape in southwestern Germany, where biodiversity has a high social value. Our results indicate an increasing consumption of wood and supply of biodiversity (up to 38.4 %) until the end of the century. Moreover, climate change may affect forest productivity, optimal harvesting rates and taxation schemes. Crucially, current management is unable to capture the adequate social value of biodiversity and is inefficient under climate change. Policy mechanisms are therefore required to correct biodiversity provision in temperate forest landscapes. [ABSTRACT FROM AUTHOR]