Economic growth and economic development 68

Introduction to Modern Economic Growth k(t+1) 45° sf(k(t))+(1–δ)k(t) k* k* k(t) Figure 2.2 Determination of the steady-state capital-labor ratio in the Solow model without population growth and technological change ignore this intersection throughout This is for a number of reasons First, k = is a steady-state equilibrium only when f (0) = 0, which corresponds to the case where capital is an essential factor, meaning that if K (t) = 0, then output is equal to zero irrespective of the amount of labor and the level of technology However, if capital is not essential, f (0) will be positive and k = will cease to be a steady state equilibrium (a stationary point of the difference equation (2.16)) This is illustrated in Figure 2.3, which draws (2.16) for the case where f (0) = ε for any ε > Second, as we will see below, this intersection, even when it exists, is an unstable point, thus the economy would never travel towards this point starting with K (0) > Third, this intersection has no economic interest for us An alternative visual representation of the steady state is to view it as the intersection between a ray through the origin with slope δ (representing the function δk) and the function sf (k) Figure 2.4 shows this picture, which is also useful for 54