In the model where the state of technology does not change what determines the steady state output per worker?
In the model where the state of technology does not change, the steady state output per worker is determined by the level of capital per worker. This is because in this model, output depends on the productivity of labor and the stock of capital. As capital accumulates, the productivity of labor increases, leading to higher output per worker. However, as the stock of capital approaches a certain level, the marginal productivity of additional capital decreases, eventually leading to a steady state level of output per worker.
In a model where the state of technology does not change, the steady state output per worker is determined by the level of capital per worker. In this type of model, the key factor of production is capital, and the level of output per worker depends on the amount of capital each worker has access to.
In this model, the production function typically takes the form of a simplified version of the Cobb-Douglas production function, with output (Y) being a function of capital (K) and labor (L). It can be represented as Y = A * K^α * L^(1-α), where A represents the level of technology, α is the output elasticity of capital, and (1-α) is the output elasticity of labor.
In the steady state, the level of capital per worker (K/L) remains constant, meaning that investment in new capital is equal to depreciation. In this state, output per worker (Y/L) is also constant. Therefore, in a model with no technological change, the level of output per worker in the steady state is solely determined by the amount of capital per worker.