Question 2 Consider an economy with n = 20 goods, with sector 1 producing good 1, sector 2 producing good 2 and so on. For the representative consumer of the economy, all 20 goods are weighted equally. The economy has _ = 4000 units of labour which is supplied by the representative consumer. Each sector has a competitive fringe of firms. Initially firms in all sectors use the traditional mode of production in which 1 unit of labour can produce 1 unit of good and the wage is 1. There is a new technology (the modern mode) in which 1 unit of labour can produce t = 4 units of the good. The modern mode pays wage 1 + v = 1 + 3 =4 (so v = 3). (a) [6 points] First suppose no investment is required for the modern mode and once a sector adopts the modern mode, all firms in the competitive fringe of that sector have the modern mode. In this case, determine the income of the economy and the demand for each good when 10 out of 20 sectors adopt the modern mode. b) [10 points] Now suppose the modern mode requires an initial employment of F = 30 units of labour. Assume that in each sector, there is a modern firm that can adopt the modern mode by making this initial employment of F units of labour. Because the wage in modern mode is 1 + v, the cost of investment is (1 + v)F [recall that we are given 1 + v = 4 and F= 30]. In this case we say a sector is "industrialized" if the modern firm of that sector makes the investment and adopts the modern mode. Once the modern firm in a sector adopts the modern mode, all other firms in the fringe are driven out of the market