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How many immigrants with less than university education, for a given immigration quota, maximise economic output? The answer is simple—zero—in the canonical model of the labour market, where the marginal product of a university-educated immigrant is always higher. We build an alternative model, following Jones (2005), in which national production occurs through a set of Leontief production functions that shift over time with technological change. This model, more consistent with historical data from Australia, implies a positive output-maximising supply of vocationally-skilled immigration, which we estimate for likely scenarios through the year 2050. Australian demand for vocationally-skilled workers will substantially exceed native supply, especially of fundamental workers performing tasks that do not require college education but are difficult to automate or offshore. Historical patterns of growth and technological change imply a demand-supply gap of two million vocationally-skilled workers by 2050. Australia can maximise future output with expanded vocationally skilled labour mobility (settler or temporary), especially by focusing on labour supply from the Pacific Islands.