Suppose income earned from investments in capital is taxed at a proportional rate (. Faced with this tax, investment occurs up to the point where the capital stock K' satisfies (1-!)MPpr = r+d, whereris the real interest rate and d is the rate at which capital depreciates over time. The production function is Y = VK VN, so the marginal products of capital and labour are MP* = 1/(2vk) and MPN = vk/2. where k = K/N denotes the capital-labour ratio. Find the steady-state capital-labour ratio k in terms of r. d, and the tax rate I (noting that k = k' implies MPpr = MPk). The government redistributes the revenue [MP, from the tax on capital to supplement the incomes of workers. Each worker receives real income m = w + IMP,k, where w = MPwy is the real wage paid by firms, and IMP,k is the amount of capital tax revenue received per worker. The government chooses the tax rate I with the goal of maximizing the real income m of workers. Assume that the real interest rate / remains constant, and the capital-labour ratio k adjusts so that (1 - [)MPp =/ + d holds. Find the value of [ that best achieves the government's objective