Imagine an economy with two people: a worker and a capitalist. The worker supplies L units of labor and saves fraction s,, of its labor income and fraction s. of its capital income. The capitalist does not work and saves fraction s. of its income. Production in this economy occurs via the production function F(K,L)=K\"L'~@ and capital accumulates according to the capital accumulation equation Kt-ll (1 - J)Kt + It Denote the wage by w; and the interest rate (amount savers are paid per unit of capital) by r;. Both factors of production are paid their marginal product. 1. Derive expressions for the wage and interest rate in terms of K;, L, and parameters. 2. Derive an expression for investment in terms of output Y; and parameters. 3. Write the steady state capital / output ratio in terms of parameters (that is, derive this economy's Harrod-Domar-Solow equation). 4. Suppose L = 1.5, a = 0.3, 6 = 0.08, s,, = 0.1, and s, = 0.4. What are steady state capital and output