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Introduction to Modern Economic Growth in the production process, making the production process itself more productive Alternatively, the knowledge stock of the economy could be a function of the cumulative output that the economy has produced up to now, thus giving it more of a flavor of “learning-by-doing” In any case, substituting for (11.35) into (11.34) and using the fact that all firms are functioning at the same capital-effective labor ratio, we obtain the production function of the representative firm as Y (t) = F (K (t) , BK (t) L) Using the fact that F (·, ·) is homogeneous of degree 1, we have Y (t) = F (1, BL) K (t) = f˜ (L) Output per capita can therefore be written as: Y (t) L Y (t) K (t) = K (t) L = k (t) f˜ (L) , y (t) ≡ where again k (t) ≡ K (t) /L is the capital-labor ratio in the economy As in the standard growth model, marginal products and factor prices can be expressed in terms of the normalized production function, now f˜ (L) In particular, we have (11.36) w (t) = K (t) f˜0 (L) and (11.37) R (t) = R = f˜ (L) − Lf˜0 (L) , which is constant 11.4.2 Equilibrium An equilibrium is defined similarly to the neoclassical growth model, as a path of consumption and capital stock for the economy, [C (t) , K (t)]∞ t=0 that maximize the utility of the representative household and wage and rental rates 523
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