In an economy characterized by a Cobb-Douglas production function (without technical progress), labour's share of income is \(70 \%\) and the depreciation rate is \(3 \%\) per annum. The economy is in a steady state with GDP growth at \(4 \%\) per year and with a capital output ratio of 2. Find the savings rate and the marginal product of capital. At time \(t\) the savings rate in this economy increases to a new constant level, with the outcome that the economy converges to the Golden Rule steady state. What are the new savings rate, capital output ratio and marginal product of capital? Use diagrams with time on the horizontal axis to sketch the path of the capital-output ratio, the marginal product of capital and of consumption per unit of labour.