We introduce a model of technological growth as allowing for greater maximum productivity at the cost of increased complexity, and calibrate it to the distribution of US firms. Complex production functions, like those producing Swiss watches or smartphones require a large amount of strongly complementary inputs. For the economy as a whole, increased complexity creates and exacerbates bottlenecks which slow growth and increase inequality. At the firm level, complexity creates a Pareto-like distribution of firm profits, size and productivity. When firms select a too-complex production function it will switch to a less complex one in subsequent periods, in an illustration of Le Chatelier’s principle. We calibrate the model and show it can be used to explain several macroeconomic stylized facts such as slow growth, and changes in the moments of the firm size distribution by industry.