which imply that the elasticity of substitution must be asymptotically equal to one. where denotes time, is the elasticity of output with respect to capital, and represents total production. refers to labor-augmenting technology or “knowledge”, thus represents effective labor. All factors of production are fully employed, and initial values , , and are given. The number of workers, i.e. labor, as well as the level of technology grow exogenously at rates and , respectively: The number of effective units of labor, , therefore grows at rate . Meanwhile, the stock of capital depreciates over time at a constant rate . However, only a fraction of the output ( with ) is consumed, leaving a saved share for investment. This dynamic is expressed through the following differential equation: where is shorthand for , the derivative with respect to time. Derivative with respect to time means that it is the change in capital stock—output that is neither consumed nor used to replace worn-out old capital goods is net investment. Since the production function has constant returns to scale, it can be written as output per effective unit of labour , which is a measure for wealth creation: The main interest of the model is the dynamics of capital intensity , the capital stock per unit of effective labour. Its behaviour over time is given by the key equation of the Solow–Swan model: The first term, , is the actual investment per unit of effective labour: the fraction of the output per unit of effective labour that is saved and invested. The second term, , is the “break-even investment”: the amount of investment that must be invested to prevent from falling. The equation implies that converges to a steady-state value of , defined by , at which there is neither an increase nor a decrease of capital intensity: at which the stock of capital and effective labour are growing at rate . Likewise, it is possible to calculate the steady-state of created wealth that corresponds with : By assumption of constant returns, output is also growing at that rate. In essence, the Solow–Swan model predicts that an economy will converge to a balanced-growth equilibrium, regardless of its starting point. In this situation, the growth of output per worker is determined solely by the rate of technological progress. Since, by definition, , at the equilibrium we have Therefore, at the equilibrium, the capital/output ratio