In neoclassical growth models, the long-run rate of growth is exogenously determined by either assuming a savings rate (the Solow model) or a rate of technical progress. However, this begs the question as the savings rate and rate of technological progress remain unexplained.
Endogenous growth theory tries to overcome this shortcoming by building macroeconomic models out of microeconomic foundations. Households are assumed to maximize utility subject to budget constraints while firms maximize profits. Crucial importance is usually given to the production of new technologies and human capital. The engine for growth can be as simple as a constant return to scale production function (the AK model) or more complicated set ups with spillover effects, increasing numbers of goods, increasing qualities, etc.
Endogenous growth theory demonstrates that policy measures can have an impact on the long-run growth rate of an economy. For example, subsidies on research and development or education increase the growth rate in some endogenous growth models by increasing the incentive to innovate.
Often endogenous growth theory assumes constant marginal product of capital at the aggregate level, or at least that the limit of the marginal product of capital does not tend towards zero. This does not imply that larger firms will be more productive than small ones, because at the firm level the marginal product of capital is still diminishing. Therefore, it is possible to construct endogenous growth models with perfect competition. However, in many endogenous growth models the assumption of perfect competition is relaxed, and some degree of monopoly power is thought to exist. Generally monopoly power in these models comes from the holding of patents. These are models with two sectors, producers of final output and an R&D sector. The R&D sector develops ideas that they are granted a monopoly over. R&D firms are assumed to be able to make monopoly profits selling ideas to production firms, but the free entry condition means that these profits are dissipated on R&D spending.
One of the main failings of endogenous growth theories is the collective failure to explain conditional convergence reported in the empirical literature. Another frequent critique concerns the cornerstone assumption of diminishing returns to capital. Some contend that new growth theory has proven no more successful than exogenous growth theory in explaining the income divergence between the developing and developed worlds (despite usually being more complex).
In a 1994 speech in Britain the then Labour Party Shadow Chancellor Gordon Brown referred to post neo-classical endogenous growth theory, a phrase (humorously) commented on by Michael Heseltine as being the product of his special adviser Ed Balls showing off, by saying "It's not Brown, it's balls"