The expression for total output and the dynamics of capital per worker are given by the following expressions: Y = AKᵃL¹⁻ᵃ Δk = sy - k , where A is the exogenous Solow residual, y is output per worker, and is the depreciation rate of capital.(a) Using the information given above, find the fundamental Solow equation. Find an expression for steady-state capital per worker. (b) What happens to steady-state capital if the depreciation rate goes up? (c) Suppose that this economy consists of two types of households: laborers and capitalists. Capitalists own all the capital stock K and are paid a rental rate equal to the marginal product of capital. Find an expression for their share of national income. (d) Assume that laborers save none of their income. If capitalists save 30% of their income, the parameter α = 0.3, and the parameter δ = 0.1, what is the aggregate saving rate s? Will income inequality between capitalists and laborers worsen over time?
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