1. Consider the CES production function with labor and capital as inputs. Suppose that labor and capital markets are perfectly competitive. Y = ( (1 - a) [ ) + ( ak ) 8 - 1 (a) [10 points] Show that the elasticity of substitution aln(K/L) _ In(r/w) = 0 E [0, 00). (b) [10 points] Derive wage (w) and interest rate (r) and show that Or/ (K/L) 0. (c) [10 points] Derive capital's share of income in terms of wealth to income ratio (Y / K). Under what conditions an increase in wealth to income ratio leads to an increase in capital's share of income