<p>This paper analyses the labour-market and inequality implications of a carbon tax in a framework with skills heterogeneity and up-skilling opportunities. Our model extends the standard Two-Agent New Keynesian (TANK) setup by including green and brown firms, skilled and unskilled workers, and human-capital accumulation. We find that a gradual increase in the carbon price, designed to achieve full decarbonisation by 2050, produces heterogeneous effects across households: (i) skilled households reduce their labour supply in the short run across both sectors, opting instead to invest immediately in green up-skilling; (ii) unskilled households, driven by the income effect, increase hours worked in both sectors; and (iii) skilled households reap higher wages in the green sector, thereby exacerbating inequality. Neglecting the role of skills heterogeneity and up-skilling investment suggests that this policy has greater negative effects on labour income, consumption and output in both the short and the long run. Our findings underscore the importance of incorporating these labour-market features for a comprehensive assessment of the aggregate, sectoral and distributional effects of a carbon tax.</p>